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Volumn 95, Issue , 2016, Pages

Iterative solution of large sparse systems of equations

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EID: 85067973190     PISSN: 00665452     EISSN: 2196968X     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (119)

References (417)
  • 1
    • 33947688091 scopus 로고
    • Zur Konvergenz des Peaceman-Rachford-Verfahrens
    • Alefeld, G.: Zur Konvergenz des Peaceman-Rachford-Verfahrens. Numer. Math. 26, 409– 419 (1976)
    • (1976) Numer. Math. , vol.26 , pp. 409-419
    • Alefeld, G.1
  • 2
    • 34250233247 scopus 로고
    • On the convergence of the symmetric SOR method for matrices with red-black ordering
    • Alefeld, G.: On the convergence of the symmetric SOR method for matrices with red-black ordering. Numer. Math. 39, 113–117 (1982)
    • (1982) Numer. Math. , vol.39 , pp. 113-117
    • Alefeld, G.1
  • 3
    • 0041907117 scopus 로고
    • Zur Konvergenz des symmetrischen Relaxationsverfahrens
    • Alefeld, G., Varga, R.S.: Zur Konvergenz des symmetrischen Relaxationsverfahrens. Numer. Math. 25, 291–295 (1976)
    • (1976) Numer. Math. , vol.25 , pp. 291-295
    • Alefeld, G.1    Varga, R.S.2
  • 4
    • 85067952114 scopus 로고    scopus 로고
    • On a problem decomposition for semilinear nearly symmetric elliptic equations
    • pp
    • Allgower, E., Böhmer, K., Zhen, M.: On a problem decomposition for semilinear nearly symmetric elliptic equations. In: Hackbusch [187], pp. 1–17
    • Hackbusch , vol.187 , pp. 1-17
    • Allgower, E.1    Böhmer, K.2    Zhen, M.3
  • 5
    • 85027931123 scopus 로고    scopus 로고
    • Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs
    • Andreev, R., Tobler, C.: Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs. Numer. Linear Algebra Appl. 22, 317– 337 (2015)
    • (2015) Numer. Linear Algebra Appl. , vol.22 , pp. 317-337
    • Andreev, R.1    Tobler, C.2
  • 7
    • 0001581067 scopus 로고
    • Adaptive polynomial preconditioning for Hermitian indefinite linear systems
    • Ashby, S.F., Manteuffel, T.A., Saylor, P.E.: Adaptive polynomial preconditioning for Hermitian indefinite linear systems. BIT 29, 583–609 (1989)
    • (1989) BIT , vol.29 , pp. 583-609
    • Ashby, S.F.1    Manteuffel, T.A.2    Saylor, P.E.3
  • 8
    • 0040354573 scopus 로고
    • An iterative method of solving elliptic net problems
    • Astrachancev, G.P.: An iterative method of solving elliptic net problems. USSR Comput. Math. Math. Phys. 11,2, 171–182 (1971)
    • (1971) USSR Comput. Math. Math. Phys. , vol.11 , Issue.2 , pp. 171-182
    • Astrachancev, G.P.1
  • 9
    • 0000773206 scopus 로고
    • Methods of fictitious domains for a second-order elliptic equation with natural boundary conditions
    • Astrachancev, G.P.: Methods of fictitious domains for a second-order elliptic equation with natural boundary conditions. USSR Comput. Math. Math. Phys. 18, 114–121 (1978)
    • (1978) USSR Comput. Math. Math. Phys. , vol.18 , pp. 114-121
    • Astrachancev, G.P.1
  • 11
    • 0008508665 scopus 로고
    • On algebraic multilevel iteration methods for selfadjoint elliptic problems with anisotropy
    • pp
    • Axelsson, O.: On algebraic multilevel iteration methods for selfadjoint elliptic problems with anisotropy. Rend. Semin. Mat. Politec. Torino pp. 31–61 (1991)
    • (1991) Rend. Semin. Mat. Politec. Torino , pp. 31-61
    • Axelsson, O.1
  • 12
    • 85067974665 scopus 로고    scopus 로고
    • Iterative Solution Methods. Cambridge Univ. Press (1994)
    • Axelsson, O.: Iterative Solution Methods. Cambridge Univ. Press (1994). Reprinted 1996
    • (1996) Reprinted
    • Axelsson, O.1
  • 14
    • 0002622213 scopus 로고
    • On some versions of incomplete block-matrix factorization iterative methods
    • Axelsson, O., Brinkkemper, S., Il’in, V.P.: On some versions of incomplete block-matrix factorization iterative methods. Linear Algebra Appl. 58, 3–15 (1984)
    • (1984) Linear Algebra Appl , vol.58 , pp. 3-15
    • Axelsson, O.1    Brinkkemper, S.2    Il’In, V.P.3
  • 16
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods, part I
    • Axelsson, O., Vassilevski, P.: Algebraic multilevel preconditioning methods, part I. Numer. Math. 56, 157–177 (1989)
    • (1989) Numer. Math. , vol.56 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.2
  • 17
    • 0001573921 scopus 로고
    • Algebraic multilevel preconditioning methods, part II
    • Axelsson, O., Vassilevski, P.: Algebraic multilevel preconditioning methods, part II. SIAM J. Numer. Anal. 27, 1569–1590 (1990)
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1569-1590
    • Axelsson, O.1    Vassilevski, P.2
  • 18
    • 0001116752 scopus 로고
    • A black box generalized CG solver with inner iterations and variable-step preconditioning
    • Axelsson, O., Vassilevski, P.: A black box generalized CG solver with inner iterations and variable-step preconditioning. SIAM J. Matrix Anal. Appl. 12, 625–644 (1991)
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 625-644
    • Axelsson, O.1    Vassilevski, P.2
  • 19
    • 0038893486 scopus 로고    scopus 로고
    • Construction of variable-step preconditioners for inner-outer iteration methods
    • ], pp
    • Axelsson, O., Vassilevski, P.: Construction of variable-step preconditioners for inner-outer iteration methods. In: Beauwens and de Groen [38], pp. 1–14
    • Beauwens and De Groen , vol.38 , pp. 1-14
    • Axelsson, O.1    Vassilevski, P.2
  • 20
    • 85067911580 scopus 로고
    • The mathematical foundation of the finite element method with applications to partial differential equations. Academic Press
    • Aziz, A.K. (ed.), Maryland, Jun
    • Aziz, A.K. (ed.): The mathematical foundation of the finite element method with applications to partial differential equations. Academic Press, New York (1972). (Maryland, Jun. 1972)
    • (1972) New York , vol.1972
  • 21
    • 0039813047 scopus 로고
    • Über Schwarzsche Algorithmen in partiellen Differentialgleichungen der mathematischen Physik
    • Babuška, I.: Über Schwarzsche Algorithmen in partiellen Differentialgleichungen der mathematischen Physik. ZAMM 37, 243–245 (1957)
    • (1957) ZAMM , vol.37 , pp. 243-245
    • Babuška, I.1
  • 22
    • 85067988286 scopus 로고
    • Mathematical programming, the state of art. Springer, Berlin (1983)
    • Bachem, A., Grötschel, M., Korte, B. (eds.), Aug
    • Bachem, A., Grötschel, M., Korte, B. (eds.): Mathematical programming, the state of art. Springer, Berlin (1983). (Bonn, Aug. 1982)
    • (1982) (Bonn
  • 23
    • 0000811219 scopus 로고
    • On the convergence of a relaxation method with natural constraints on the elliptic operator
    • Bakhvalov, N.S.: On the convergence of a relaxation method with natural constraints on the elliptic operator. USSR Comput. Math. Math. Phys. 6(5), 101–135 (1966)
    • (1966) USSR Comput. Math. Math. Phys. , vol.6 , Issue.5 , pp. 101-135
    • Bakhvalov, N.S.1
  • 24
    • 84870908752 scopus 로고    scopus 로고
    • A projection method to solve linear systems in tensor format
    • Ballani, J., Grasedyck, L.: A projection method to solve linear systems in tensor format. Numer. Linear Algebra Appl. 20, 27–43 (2013)
    • (2013) Numer. Linear Algebra Appl. , vol.20 , pp. 27-43
    • Ballani, J.1    Grasedyck, L.2
  • 25
    • 85067931100 scopus 로고    scopus 로고
    • Marching algorithms and block Gaussian elimination
    • Bank, R.E.: Marching algorithms and block Gaussian elimination. In: Bunch and Rose [86], pp. 293–307
    • Bunch and Rose , vol.86 , pp. 293-307
    • Bank, R.E.1
  • 26
    • 21344492025 scopus 로고
    • An analysis of the composite step biconjugate gradient method
    • Bank, R.E., Chan, T.F.: An analysis of the composite step biconjugate gradient method. Numer. Math. 66, 295–319 (1993)
    • (1993) Numer. Math. , vol.66 , pp. 295-319
    • Bank, R.E.1    Chan, T.F.2
  • 27
    • 0022107998 scopus 로고
    • Sharp estimates for multigrid rates of convergence with general smoothing and acceleration
    • Bank, R.E., Douglas, C.C.: Sharp estimates for multigrid rates of convergence with general smoothing and acceleration. SIAM J. Numer. Anal. 22, 617–633 (1985)
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 617-633
    • Bank, R.E.1    Douglas, C.C.2
  • 29
    • 84966225317 scopus 로고
    • An optimal order process for solving elliptic finite element equations
    • Bank, R.E., Dupont, T.F.: An optimal order process for solving elliptic finite element equations. Math. Comp. 36, 35–51 (1981)
    • (1981) Math. Comp. , vol.36 , pp. 35-51
    • Bank, R.E.1    Dupont, T.F.2
  • 30
    • 0001377512 scopus 로고
    • The hierarchical basis multigrid method
    • Bank, R.E., Dupont, T.F., Yserentant, H.: The hierarchical basis multigrid method. Math. Comp. 52, 427–458 (1988)
    • (1988) Math. Comp. , vol.52 , pp. 427-458
    • Bank, R.E.1    Dupont, T.F.2    Yserentant, H.3
  • 32
    • 0000728755 scopus 로고
    • On the conditioning of finite element equations with highly refined meshes
    • Bank, R.E., Scott, L.R.: On the conditioning of finite element equations with highly refined meshes. SIAM J. Numer. Anal. 26, 1383–1394 (1989)
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1383-1394
    • Bank, R.E.1    Scott, L.R.2
  • 34
    • 0031625842 scopus 로고    scopus 로고
    • Additive and multiplicative multi-grid – a comparison
    • Bastian, P., Hackbusch, W., Wittum, G.: Additive and multiplicative multi-grid – a comparison. Computing 60, 345–364 (1998)
    • (1998) Computing , vol.60 , pp. 345-364
    • Bastian, P.1    Hackbusch, W.2    Wittum, G.3
  • 35
    • 55749093820 scopus 로고    scopus 로고
    • Low-rank solution of data-sparse Sylvester equations
    • Baur, U.: Low-rank solution of data-sparse Sylvester equations. Numer. Linear Algebra Appl. 15, 837–851 (2008)
    • (2008) Numer. Linear Algebra Appl. , vol.15 , pp. 837-851
    • Baur, U.1
  • 36
    • 33751525432 scopus 로고    scopus 로고
    • Factorized solution of Lyapupov equations based on hierarchical matrix arithmetic
    • Baur, U., Benner, P.: Factorized solution of Lyapupov equations based on hierarchical matrix arithmetic. Computing 78, 211–234 (2006)
    • (2006) Computing , vol.78 , pp. 211-234
    • Baur, U.1    Benner, P.2
  • 37
    • 0039799272 scopus 로고
    • Approximate factorizations with s/p consistently ordered M-factors
    • Beauwens, R.: Approximate factorizations with s/p consistently ordered M-factors. BIT 29, 658–681 (1989)
    • (1989) BIT , vol.29 , pp. 658-681
    • Beauwens, R.1
  • 38
    • 85067926904 scopus 로고
    • Iterative Methods in Linear Algebra. North-Holland
    • Beauwens, R., de Groen, P. (eds.), Brussels, April
    • Beauwens, R., de Groen, P. (eds.): Iterative Methods in Linear Algebra. North-Holland, Amsterdam (1992). (Brussels, April 1991)
    • (1991) Amsterdam , vol.1992
  • 40
    • 84878964797 scopus 로고    scopus 로고
    • Low rank methods for a class of generalized Lyapunov equations and related issues
    • Benner, P., Breiten, T.: Low rank methods for a class of generalized Lyapunov equations and related issues. Numer. Math. 124, 441–470 (2013)
    • (2013) Numer. Math. , vol.124 , pp. 441-470
    • Benner, P.1    Breiten, T.2
  • 41
    • 55549085348 scopus 로고    scopus 로고
    • Gianfranco Cimmino’s contributions to numerical mathematics
    • pp., Seminario di Analisi Matematica, Dipartimento di Matematica dell’Universit di Bologna
    • Benzi, M.: Gianfranco Cimmino’s contributions to numerical mathematics. In: Ciclo di Conferenze in Ricordo di Gianfranco Cimmino, March-May 2004, pp. 87–109. Seminario di Analisi Matematica, Dipartimento di Matematica dell’Universit di Bologna (2005)
    • (2005) Ciclo Di Conferenze in Ricordo Di Gianfranco Cimmino, March-May 2004 , pp. 87-109
    • Benzi, M.1
  • 42
    • 0142087843 scopus 로고    scopus 로고
    • A robust incomplete factorization preconditioner for positive definite matrices
    • Benzi, M., Tůma, M.: A robust incomplete factorization preconditioner for positive definite matrices. Numer. Linear Algebra Appl. 10, 385–400 (2003)
    • (2003) Numer. Linear Algebra Appl. , vol.10 , pp. 385-400
    • Benzi, M.1    Tůma, M.2
  • 46
    • 0016036113 scopus 로고    scopus 로고
    • Cones and iterative methods for best least squares solutions of linear systems
    • Berman, A., Plemmons, R.J.: Cones and iterative methods for best least squares solutions of linear systems. SIAM J. Numer. Anal. 11, 145–154 (2006)
    • (2006) SIAM J. Numer. Anal. , vol.11 , pp. 145-154
    • Berman, A.1    Plemmons, R.J.2
  • 51
    • 0008765509 scopus 로고
    • On the spectra of sums of orthogonal projections with applications to parallel computing
    • Bjørstad, P.E., Mandel, J.L.: On the spectra of sums of orthogonal projections with applications to parallel computing. BIT 31, 76–88 (1991)
    • (1991) BIT , vol.31 , pp. 76-88
    • Bjørstad, P.E.1    Mandel, J.L.2
  • 52
    • 0022918065 scopus 로고
    • Iterative methods for the solution of elliptic problems on regions partitioned into substructures
    • Bjørstad, P.E., Widlund, O.B.: Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23, 1097–1120 (1986)
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1097-1120
    • Bjørstad, P.E.1    Widlund, O.B.2
  • 53
    • 0025474829 scopus 로고
    • On finite element domain imbedding methods
    • Börgers, C., Widlund, O.B.: On finite element domain imbedding methods. SIAM J. Numer. Anal. 27, 963–978 (1990)
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 963-978
    • Börgers, C.1    Widlund, O.B.2
  • 54
    • 84960916076 scopus 로고    scopus 로고
    • Efficient Numerical Methods for Non-local Operators. EMS, Zürich (2010)
    • Börm, S.: Efficient Numerical Methods for Non-local Operators. EMS, Zürich (2010). Corrected 2nd printing, 2013
    • (2013) Corrected 2Nd Printing
    • Börm, S.1
  • 55
    • 84923564995 scopus 로고    scopus 로고
    • Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates
    • published 2015
    • Börm, S., Reimer, K.: Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates. Comput. Vis. Sci. 16, 247–258 (2013) [published 2015]
    • (2013) Comput. Vis. Sci. , vol.16 , pp. 247-258
    • Börm, S.1    Reimer, K.2
  • 56
    • 0030369254 scopus 로고    scopus 로고
    • The cascadic multigrid method for elliptic problems
    • Bornemann, F., Deuflhard, P.: The cascadic multigrid method for elliptic problems. Numer. Math. 75, 135–152 (1996)
    • (1996) Numer. Math. , vol.75 , pp. 135-152
    • Bornemann, F.1    Deuflhard, P.2
  • 57
    • 21144473187 scopus 로고
    • A basic norm equivalence for the theory of multilevel methods
    • Bornemann, F., Yserentant, H.: A basic norm equivalence for the theory of multilevel methods. Numer. Math. 64, 455–476 (1993)
    • (1993) Numer. Math. , vol.64 , pp. 455-476
    • Bornemann, F.1    Yserentant, H.2
  • 58
    • 0012672225 scopus 로고
    • The contraction number of a multigrid method for solving the Poisson equation
    • Braess, D.: The contraction number of a multigrid method for solving the Poisson equation. Numer. Math. 37, 387–404 (1981)
    • (1981) Numer. Math. , vol.37 , pp. 387-404
    • Braess, D.1
  • 59
    • 84966218274 scopus 로고
    • The convergence rate of a multigrid method with Gauß-Seidel relaxation for the Poisson equation
    • Braess, D.: The convergence rate of a multigrid method with Gauß-Seidel relaxation for the Poisson equation. Math. Comp. 42, 505–386 (1984)
    • (1984) Math. Comp. , vol.42 , pp. 505-386
    • Braess, D.1
  • 61
    • 0010038766 scopus 로고    scopus 로고
    • On the combination of the multigrid method and conjugate gradients
    • ], pp
    • Braess, D.: On the combination of the multigrid method and conjugate gradients. In: Hack-busch and Trottenberg [206], pp. 52–64
    • Hack-Busch and Trottenberg , vol.206 , pp. 52-64
    • Braess, D.1
  • 62
    • 0348086589 scopus 로고
    • A multigrid method for the membran problem
    • Braess, D.: A multigrid method for the membran problem. Comput. Mech. 3, 321–329 (1988)
    • (1988) Comput. Mech. , vol.3 , pp. 321-329
    • Braess, D.1
  • 64
    • 0032653914 scopus 로고    scopus 로고
    • Grid transfer for nonconforming FE-discretisations with application to non-matching grids
    • Braess, D., Dryja, M., Hackbusch, W.: Grid transfer for nonconforming FE-discretisations with application to non-matching grids. Computing 63, 1–25 (1999)
    • (1999) Computing , vol.63 , pp. 1-25
    • Braess, D.1    Dryja, M.2    Hackbusch, W.3
  • 65
    • 0000671861 scopus 로고
    • A new convergence proof for the multigrid method including the V-cycle
    • Braess, D., Hackbusch, W.: A new convergence proof for the multigrid method including the V-cycle. SIAM J. Numer. Anal. 20, 967–975 (1983)
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 967-975
    • Braess, D.1    Hackbusch, W.2
  • 66
    • 26444558083 scopus 로고    scopus 로고
    • Approximation of 1/x by exponential sums in [1, ∞)
    • Braess, D., Hackbusch, W.: Approximation of 1/x by exponential sums in [1, ∞). IMA J. Numer. Anal. 25, 685–697 (2005)
    • (2005) IMA J. Numer. Anal. , vol.25 , pp. 685-697
    • Braess, D.1    Hackbusch, W.2
  • 67
    • 84892819022 scopus 로고    scopus 로고
    • On the efficient computation of high-dimensional integrals and the approximation by exponential sums
    • Braess, D., Hackbusch, W.: On the efficient computation of high-dimensional integrals and the approximation by exponential sums. In: DeVore and Kunoth [107], pp. 39–74
    • Devore and Kunoth , vol.107 , pp. 39-74
    • Braess, D.1    Hackbusch, W.2
  • 68
    • 85067994536 scopus 로고
    • Advances in Multi-Grid Methods, Notes on Numerical Fluid Mechanics, Vol. 11. Vieweg
    • (eds.), Oberwol-fach, Dec
    • Braess, D., Hackbusch, W., Trottenberg, U. (eds.): Advances in Multi-Grid Methods, Notes on Numerical Fluid Mechanics, Vol. 11. Vieweg, Braunschweig (1985). (Oberwol-fach, Dec. 1984)
    • (1984) Braunschweig , vol.1985
    • Braess, D.1    Hackbusch, W.2    Trottenberg, U.3
  • 69
    • 0039674977 scopus 로고
    • Über die numerische Behandlung von Integralgleichungen nach der Quadra-turformelmethode
    • Brakhage, H.: Über die numerische Behandlung von Integralgleichungen nach der Quadra-turformelmethode. Numer. Math. 2, 183–196 (1960)
    • (1960) Numer. Math. , vol.2 , pp. 183-196
    • Brakhage, H.1
  • 70
    • 84966199070 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, part I
    • Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring, part I. Math. Comp. 47, 103–134 (1986)
    • (1986) Math. Comp. , vol.47 , pp. 103-134
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 71
    • 84966251372 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, part II
    • Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring, part II. Math. Comp. 49, 1–16 (1987)
    • (1987) Math. Comp. , vol.49 , pp. 1-16
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 72
    • 84966211313 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, part III
    • Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring, part III. Math. Comp. 51, 415–430 (1988)
    • (1988) Math. Comp. , vol.51 , pp. 415-430
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 73
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, part IV
    • Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring, part IV. Math. Comp. 53, 1–24 (1989)
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 74
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumptions
    • Bramble, J.H., Pasciak, J.E., Wang, J., Xu, J.: Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comp. 57, 23–45 (1991)
    • (1991) Math. Comp. , vol.57 , pp. 23-45
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 75
    • 84966234078 scopus 로고
    • The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems
    • Bramble, J.H., Pasciak, J.E., Xu, J.: The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems. Math. Comp. 51, 389–414 (1988)
    • (1988) Math. Comp. , vol.51 , pp. 389-414
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 76
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • Bramble, J.H., Pasciak, J.E., Xu, J.: Parallel multilevel preconditioners. Math. Comp. 55, 1–22 (1990)
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 77
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31, 333–390 (1977)
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 79
    • 0036013521 scopus 로고    scopus 로고
    • Convergence of the multigrid V-cycle algorithm for second-order boundary value problems without full elliptic regularity
    • Brenner, S.C.: Convergence of the multigrid V-cycle algorithm for second-order boundary value problems without full elliptic regularity. Math. Comp. 71, 507–525 (2002)
    • (2002) Math. Comp. , vol.71 , pp. 507-525
    • Brenner, S.C.1
  • 80
    • 0142087017 scopus 로고    scopus 로고
    • An additive Schwarz preconditioner for the FETI method
    • Brenner, S.C.: An additive Schwarz preconditioner for the FETI method. Numer. Math. 94, 1–31 (2003)
    • (2003) Numer. Math. , vol.94 , pp. 1-31
    • Brenner, S.C.1
  • 81
    • 2942677350 scopus 로고    scopus 로고
    • Convergence of nonconforming V-cycle and F-cycle multigrid algorithms for second order elliptic boundary value problems
    • Brenner, S.C.: Convergence of nonconforming V-cycle and F-cycle multigrid algorithms for second order elliptic boundary value problems. Math. Comp. 73, 1041–1066 (2004)
    • (2004) Math. Comp. , vol.73 , pp. 1041-1066
    • Brenner, S.C.1
  • 84
    • 0001045889 scopus 로고
    • Numerical method for solving two-and three-dimensional diffusion equations
    • in Russian
    • Buleev, N.I.: Numerical method for solving two-and three-dimensional diffusion equations [in Russian]. Mat. Sb. 51, 227–238 (1960)
    • (1960) Mat. Sb. , vol.51 , pp. 227-238
    • Buleev, N.I.1
  • 86
    • 85067937587 scopus 로고
    • Sparse Matrix Computations. Academic Press, New York (1976). (Argonne National
    • (eds.), Sep
    • Bunch, J.R., Rose, D.J. (eds.): Sparse Matrix Computations. Academic Press, New York (1976). (Argonne National Laboratory, Sep. 1975)
    • (1975) Laboratory
    • Bunch, J.R.1    Rose, D.J.2
  • 87
    • 0004126513 scopus 로고
    • A compact non-iterative Poisson solver
    • Buneman, O.: A compact non-iterative Poisson solver. SUIPR Report 294, Stanford University (1969)
    • (1969) SUIPR Report , vol.294
    • Buneman, O.1
  • 88
    • 0040470324 scopus 로고    scopus 로고
    • Theorems of Stein–Rosenberg type
    • Buoni, J.J., Varga, R.S.: Theorems of Stein–Rosenberg type. In: Ansorge et al. [6], pp. 65–75
    • Ansorge , vol.6 , pp. 65-75
    • Buoni, J.J.1    Varga, R.S.2
  • 90
    • 0000161555 scopus 로고
    • On direct methods for solving Poisson’s equations
    • Buzbee, B., Golub, G.H., Nielson, C.: On direct methods for solving Poisson’s equations. SIAM J. Numer. Anal. 7, 627–656 (1970)
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 627-656
    • Buzbee, B.1    Golub, G.H.2    Nielson, C.3
  • 91
    • 2442557184 scopus 로고    scopus 로고
    • Two-frequency decomposition
    • Buzdin, A., Wittum, G.: Two-frequency decomposition. Numer. Math. 97, 269–295 (2004)
    • (2004) Numer. Math. , vol.97 , pp. 269-295
    • Buzdin, A.1    Wittum, G.2
  • 92
    • 0001743874 scopus 로고
    • Domain decomposition algorithms for indefinite elliptic problems
    • Cai, X.C., Widlund, O.B.: Domain decomposition algorithms for indefinite elliptic problems. SIAM J. Sci. Statist. Comput. 13, 243–258 (1992)
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 243-258
    • Cai, X.C.1    Widlund, O.B.2
  • 94
    • 85067965948 scopus 로고
    • Domain Decomposition Methods for Partial Differential Equations. SIAM
    • (eds.), Houston, Mar
    • Chan, T.F., Glowinski, R., Périaux, J., Widlund, O.B. (eds.): Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia (1990). (Houston, Mar. 1989)
    • (1989) Philadelphia , vol.1990
    • Chan, T.F.1    Glowinski, R.2    Périaux, J.3    Widlund, O.B.4
  • 95
    • 85067999057 scopus 로고    scopus 로고
    • Domain Decomposition Methods in Science and Engineering
    • (eds.), Chiba, Oct
    • Chan, T.F., Kako, T., Kawarada, H., Pironneau, O. (eds.): Domain Decomposition Methods in Science and Engineering. ddm.org (2001). (Chiba, Oct. 1999)
    • (1999) Ddm.Org , vol.2001
    • Chan, T.F.1    Kako, T.2    Kawarada, H.3    Pironneau, O.4
  • 97
    • 0001054069 scopus 로고
    • Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari
    • Cimmino, G.: Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari. Ricerca Scientifica ed il Progresso Tecnico 9, 326–333 (1938)
    • (1938) Ricerca Scientifica Ed Il Progresso Tecnico , vol.9 , pp. 326-333
    • Cimmino, G.1
  • 98
    • 0002576532 scopus 로고    scopus 로고
    • A generalized conjugate gradient method for nonsymmetric systems of linear equations
    • ], pp
    • Concus, P., Golub, G.H.: A generalized conjugate gradient method for nonsymmetric systems of linear equations. In: Glowinski and Lions [152], pp. 56–65
    • Glowinski and Lions , vol.152 , pp. 56-65
    • Concus, P.1    Golub, G.H.2
  • 100
    • 2942657742 scopus 로고    scopus 로고
    • Inverse inequalities on non-quasiuniform meshes and applications to the mortar element method
    • Dahmen, W., Faermann, B., Graham, I.G., Hackbusch, W., Sauter, S.A.: Inverse inequalities on non-quasiuniform meshes and applications to the mortar element method. Math. Comp. 73, 1107–1138 (2003)
    • (2003) Math. Comp. , vol.73 , pp. 1107-1138
    • Dahmen, W.1    Faermann, B.2    Graham, I.G.3    Hackbusch, W.4    Sauter, S.A.5
  • 101
    • 33845592412 scopus 로고
    • Multilevel preconditioning
    • Dahmen, W., Kunoth, A.: Multilevel preconditioning. Numer. Math. 63, 315–344 (1992)
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 102
    • 0039991521 scopus 로고
    • Extremal polynomials with applications to Richardson iteration for indefinite linear systems
    • de Boor, C., Rice, J.R.: Extremal polynomials with applications to Richardson iteration for indefinite linear systems. SIAM J. Sci. Statist. Comput. 3, 47–57 (1982)
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 47-57
    • de Boor, C.1    Rice, J.R.2
  • 104
    • 0003090969 scopus 로고
    • Matrix-dependent prolongations and restrictions in a blackbox multigrid solvers
    • de Zeeuw, P.M.: Matrix-dependent prolongations and restrictions in a blackbox multigrid solvers. J. Comput. Appl. Math. 33, 1–27 (1990)
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 1-27
    • de Zeeuw, P.M.1
  • 105
    • 0003381421 scopus 로고    scopus 로고
    • Incomplete line LU as smoother and as preconditioner
    • ], pp
    • de Zeeuw, P.M.: Incomplete line LU as smoother and as preconditioner. In: Hackbusch and Wittum [208], pp. 215–224
    • Hackbusch and Wittum , vol.208 , pp. 215-224
    • de Zeeuw, P.M.1
  • 106
    • 85067948069 scopus 로고    scopus 로고
    • Domain Decomposition Methods in Science and Engineering. CIMNE, Barcelona (2002)
    • (eds.), Oct
    • Debit, N., Garbey, M., Hoppe, R.H.W., Keyes, D.E., Kuznetsov, Y.A., Périaux, J. (eds.): Domain Decomposition Methods in Science and Engineering. CIMNE, Barcelona (2002). (Lyon, Oct. 2000)
    • (2000) (Lyon
    • Debit, N.1    Garbey, M.2    Hoppe, R.H.W.3    Keyes, D.E.4    Kuznetsov, Y.A.5    Périaux, J.6
  • 107
    • 84892815109 scopus 로고    scopus 로고
    • Multiscale, Nonlinear and Adaptive Approximation. Springer
    • (eds.), Günzburg, Oct
    • DeVore, R.A., Kunoth, A. (eds.): Multiscale, Nonlinear and Adaptive Approximation. Springer, Berlin (2009) (Günzburg, Oct. 2009)
    • (2009) Berlin , vol.2009
    • Devore, R.A.1    Kunoth, A.2
  • 108
    • 85068015186 scopus 로고    scopus 로고
    • Multigrid methods VI, Lect. Notes Comput. Sci. Eng., Vol. 14. Springer, Berlin (2000)
    • (eds.), Sep
    • Dick, E., Riemslagh, K., Vierendeels, J. (eds.): Multigrid methods VI, Lect. Notes Comput. Sci. Eng., Vol. 14. Springer, Berlin (2000). (Gent, Sep. 1999)
    • (1999) (Gent
    • Dick, E.1    Riemslagh, K.2    Vierendeels, J.3
  • 109
    • 84961218633 scopus 로고    scopus 로고
    • Domain Decomposition Methods in Science and Engineering XXII, Lect. Notes Comput. Sci. Eng., Vol. 104. Springer
    • (eds.), Lugano, Sep
    • Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.): Domain Decomposition Methods in Science and Engineering XXII, Lect. Notes Comput. Sci. Eng., Vol. 104. Springer, Cham (2016). (Lugano, Sep. 2013)
    • (2013) Cham , vol.2016
    • Dickopf, T.1    Gander, M.J.2    Halpern, L.3    Krause, R.4    Pavarino, L.F.5
  • 110
    • 2342508155 scopus 로고
    • The construction of iterative methods based on the use of spectrally equivalent operators
    • D’Jakonov, E.G.: The construction of iterative methods based on the use of spectrally equivalent operators. USSR Comput. Math. Math. Phys. 6,1, 14–46 (1966)
    • (1966) USSR Comput. Math. Math. Phys. , vol.6 , Issue.1 , pp. 14-46
    • D’Jakonov, E.G.1
  • 111
    • 0000530612 scopus 로고
    • A finite-capacitance matrix method for elliptic problems on regions partitioned into subregions
    • Dryja, M.: A finite-capacitance matrix method for elliptic problems on regions partitioned into subregions. Numer. Math. 44, 153–168 (1984)
    • (1984) Numer. Math. , vol.44 , pp. 153-168
    • Dryja, M.1
  • 113
    • 0345847793 scopus 로고    scopus 로고
    • On the nonlinear domain decomposition method
    • Dryja, M., Hackbusch, W.: On the nonlinear domain decomposition method. BIT 37, 296–311 (1997)
    • (1997) BIT , vol.37 , pp. 296-311
    • Dryja, M.1    Hackbusch, W.2
  • 114
    • 85068008421 scopus 로고    scopus 로고
    • Dryja, M., Widlund, O.B.: Towards a unified theory of domain decomposition algorithms for elliptic problems. In: Chan et al. [94], pp. 3–21
    • Dryja, M.1    Widlund, O.B.2
  • 115
    • 0002990325 scopus 로고    scopus 로고
    • Multilevel additive methods for elliptic finite element problems
    • ], pp
    • Dryja, M., Widlund, O.B.: Multilevel additive methods for elliptic finite element problems. In: Hackbusch [187], pp. 58–69
    • Hackbusch [187 , pp. 58-69
    • Dryja, M.1    Widlund, O.B.2
  • 117
    • 0000602242 scopus 로고
    • The effect of ordering on preconditioned conjugate gradients
    • Duff, I.S., Meurant, G.A.: The effect of ordering on preconditioned conjugate gradients. BIT 29, 635–657 (1989)
    • (1989) BIT , vol.29 , pp. 635-657
    • Duff, I.S.1    Meurant, G.A.2
  • 118
    • 0041126524 scopus 로고
    • Optimal successive overrelaxation iterative methods for p-cyclic matrices
    • Eiermann, M., Niethammer, W., Ruttan, A.: Optimal successive overrelaxation iterative methods for p-cyclic matrices. Numer. Math. 57, 593–606 (1990)
    • (1990) Numer. Math. , vol.57 , pp. 593-606
    • Eiermann, M.1    Niethammer, W.2    Ruttan, A.3
  • 119
    • 0000854079 scopus 로고
    • A study of semiiterative methods for non-symmetric systems of linear equations
    • Eiermann, M., Niethammer, W., Varga, R.S.: A study of semiiterative methods for non-symmetric systems of linear equations. Numer. Math. 47, 505–533 (1985)
    • (1985) Numer. Math. , vol.47 , pp. 505-533
    • Eiermann, M.1    Niethammer, W.2    Varga, R.S.3
  • 120
    • 0041603484 scopus 로고
    • Iterationsverfahren für nichtsymmetrische Gleichungssysteme und Approximationsmethoden im Komplexen
    • Eiermann, M., Niethammer, W., Varga, R.S.: Iterationsverfahren für nichtsymmetrische Gleichungssysteme und Approximationsmethoden im Komplexen. Jber. d. Dt. Math.-Verein. 89, 1–33 (1987)
    • (1987) Jber. D. Dt. Math.-Verein. , vol.89 , pp. 1-33
    • Eiermann, M.1    Niethammer, W.2    Varga, R.S.3
  • 121
    • 0001330133 scopus 로고
    • Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems
    • Elman, H.C.: Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems. BIT 29, 890–915 (1989)
    • (1989) BIT , vol.29 , pp. 890-915
    • Elman, H.C.1
  • 124
    • 84893873908 scopus 로고    scopus 로고
    • Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats
    • Espig, M., Hackbusch, W., Litvinenko, A., Matthies, H.G., Wähnert, P.: Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats. Comput. Math. Appl. 67, 818–829 (2014)
    • (2014) Comput. Math. Appl. , vol.67 , pp. 818-829
    • Espig, M.1    Hackbusch, W.2    Litvinenko, A.3    Matthies, H.G.4    Wähnert, P.5
  • 125
    • 84867502565 scopus 로고    scopus 로고
    • Variational calculus with sums of elementary tensors of fixed rank
    • Espig, M., Hackbusch, W., Rohwedder, T., Schneider, R.: Variational calculus with sums of elementary tensors of fixed rank. Numer. Math. 122, 469–488 (2012)
    • (2012) Numer. Math. , vol.122 , pp. 469-488
    • Espig, M.1    Hackbusch, W.2    Rohwedder, T.3    Schneider, R.4
  • 126
    • 84862262704 scopus 로고    scopus 로고
    • Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
    • Falcó, A., Nouy, A.: Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces. Numer. Math. 121, 503–530 (2012)
    • (2012) Numer. Math. , vol.121 , pp. 503-530
    • Falcó, A.1    Nouy, A.2
  • 127
    • 0026239487 scopus 로고
    • A method of finite element tearing and interconnecting and its parallel solution algorithm
    • Farhat, C., Roux, F.X.: A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Num. Meth. Engng. 32, 1205–1227 (1991)
    • (1991) Int. J. Num. Meth. Engng. , vol.32 , pp. 1205-1227
    • Farhat, C.1    Roux, F.X.2
  • 129
    • 84947017389 scopus 로고    scopus 로고
    • H-matrix approximability of the inverses of FEM matrices
    • Faustmann, M., Melenk, J.M., Praetorius, D.: H-matrix approximability of the inverses of FEM matrices. Numer. Math. 131, 615–642 (2015)
    • (2015) Numer. Math. , vol.131 , pp. 615-642
    • Faustmann, M.1    Melenk, J.M.2    Praetorius, D.3
  • 130
    • 85000783264 scopus 로고    scopus 로고
    • Existence of H-matrix approximants to the inverses of BEM matrices: The simple-layer operator
    • Faustmann, M., Melenk, J.M., Praetorius, D.: Existence of H-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Math. Comp. 85, 119–152 (2016)
    • (2016) Math. Comp. , vol.85 , pp. 119-152
    • Faustmann, M.1    Melenk, J.M.2    Praetorius, D.3
  • 131
    • 50549189861 scopus 로고
    • A relaxation method for solving elliptic difference equations
    • Fedorenko, R.P.: A relaxation method for solving elliptic difference equations. USSR Comput. Math. Math. Phys. 1, 1092–1096 (1961)
    • (1961) USSR Comput. Math. Math. Phys. , vol.1 , pp. 1092-1096
    • Fedorenko, R.P.1
  • 132
    • 0001038302 scopus 로고
    • The speed of convergence of one iterative process
    • Fedorenko, R.P.: The speed of convergence of one iterative process. USSR Comput. Math. Math. Phys. 4, 227–235 (1964)
    • (1964) USSR Comput. Math. Math. Phys. , vol.4 , pp. 227-235
    • Fedorenko, R.P.1
  • 134
    • 0001618930 scopus 로고
    • On the constrained Chebyshev approximation problem on ellipses
    • Fischer, B., Freund, R.W.: On the constrained Chebyshev approximation problem on ellipses. J. Approx. Theory 62, 297–315 (1990)
    • (1990) J. Approx. Theory , vol.62 , pp. 297-315
    • Fischer, B.1    Freund, R.W.2
  • 135
    • 0000480924 scopus 로고
    • Chebyshev polynomials are not always optimal
    • Fischer, B., Freund, R.W.: Chebyshev polynomials are not always optimal. J. Approx. Theory 65, 261–272 (1991)
    • (1991) J. Approx. Theory , vol.65 , pp. 261-272
    • Fischer, B.1    Freund, R.W.2
  • 138
    • 84966254155 scopus 로고
    • Solving linear algebraic equations can be interesting
    • Forsythe, G.E.: Solving linear algebraic equations can be interesting. Bull. Amer. Math. Soc. 59, 299–329 (1953)
    • (1953) Bull. Amer. Math. Soc. , vol.59 , pp. 299-329
    • Forsythe, G.E.1
  • 140
    • 0008327253 scopus 로고
    • The method of minimum iterations with minimum errors for a system of linear algebraic equations with a symmetrical matrix
    • Fridman, V.M.: The method of minimum iterations with minimum errors for a system of linear algebraic equations with a symmetrical matrix. USSR Comput. Math. Math. Phys. 2, 362–363 (1963)
    • (1963) USSR Comput. Math. Math. Phys. , vol.2 , pp. 362-363
    • Fridman, V.M.1
  • 143
    • 33845744599 scopus 로고
    • H-Splittings and two-stage iterative methods
    • Frommer, A., Szyld, D.B.: H-Splittings and two-stage iterative methods. Numer. Math. 63, 345–356 (1992)
    • (1992) Numer. Math. , vol.63 , pp. 345-356
    • Frommer, A.1    Szyld, D.B.2
  • 146
    • 85067914512 scopus 로고
    • Nachlass: Theoria interpolationis: Methodo nova tractata [1805]
    • Werke, Vol, Königliche Gesellschaft der Wissenschaft, Göttingen, Reprint by Georg Olms, Hildesheim
    • Gauss, C.F.: Nachlass: Theoria interpolationis: methodo nova tractata [1805]. In: Werke, Vol. 3, pp. 265–303. Königliche Gesellschaft der Wissenschaft, Göttingen (1866). Reprint by Georg Olms, Hildesheim, 1981
    • (1866) 3, Pp , vol.265-303 , pp. 1981
    • Gauss, C.F.1
  • 147
    • 85067969642 scopus 로고
    • Supplementum theoriae combinationis observationum erroribus minimis ob-noxiae [1826]
    • Werke, Vol, Königliche Gesellschaft der Wissenschaft, Göttingen, Reprint by Georg Olms, Hildesheim
    • Gauss, C.F.: Supplementum theoriae combinationis observationum erroribus minimis ob-noxiae [1826]. In: Werke, Vol. 4, pp. 55–93. Königliche Gesellschaft der Wissenschaft, Göttingen (1873). Reprint by Georg Olms, Hildesheim, 1981
    • (1873) 4, Pp , vol.55-93 , pp. 1981
    • Gauss, C.F.1
  • 148
    • 85067957862 scopus 로고    scopus 로고
    • Gauss, C.F.: Brief an Gerling [1823]. In: Werke, Vol. 9, pp. 278–281. Königliche Gesell-schaft der Wissenschaft, Göttingen (1903). Reprint by Georg Olms, Hildesheim, 1981. English translation in [137]
    • Gauss, C.F.1
  • 149
    • 0000264382 scopus 로고
    • Nested dissection of a regular finite element mesh
    • George, A.: Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10, 345–363 (1973)
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 345-363
    • George, A.1
  • 150
    • 85067946900 scopus 로고
    • First International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM
    • Glowinski, R., Golub, G.H., Meurant, G.A., Périaux, J. (eds.), Paris, Jan
    • Glowinski, R., Golub, G.H., Meurant, G.A., Périaux, J. (eds.): First International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia (1988). (Paris, Jan. 1987)
    • (1987) Philadelphia , vol.1988
  • 151
    • 85067913527 scopus 로고
    • Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM
    • Glowinski, R., Kuznetsov, Y.A., Meurant, G.A., Périaux, J., Widlund, O.B. (eds.), Moscow, May
    • Glowinski, R., Kuznetsov, Y.A., Meurant, G.A., Périaux, J., Widlund, O.B. (eds.): Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia (1991). (Moscow, May 1990)
    • (1990) Philadelphia , vol.1991
  • 153
    • 85067960765 scopus 로고
    • Domain Decomposition Methods in Science and Engineering. John Wiley & Sons
    • (eds.), Beijing, May
    • Glowinski, R., Périaux, J., Shi, Z.C., Widlund, O.B. (eds.): Domain Decomposition Methods in Science and Engineering. John Wiley & Sons, Strasbourg (1997). (Beijing, May 1995)
    • (1995) Strasbourg , vol.1997
    • Glowinski, R.1    Périaux, J.2    Shi, Z.C.3    Widlund, O.B.4
  • 155
    • 0024631560 scopus 로고
    • Some history of the conjugate gradient and Lanczos algorithms: 1948-1976
    • Golub, G.H., O’Leary, D.P.: Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. SIAM Rev. 31, 50–102 (1989)
    • (1989) SIAM Rev , vol.31 , pp. 50-102
    • Golub, G.H.1    O’Leary, D.P.2
  • 156
    • 0001263639 scopus 로고
    • The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems
    • Golub, G.H., Overton, M.L.: The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Numer. Math. 53, 571–593 (1988)
    • (1988) Numer. Math. , vol.53 , pp. 571-593
    • Golub, G.H.1    Overton, M.L.2
  • 157
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed. The Johns Hopkins University Press, Baltimore
    • Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd ed. The Johns Hopkins University Press, Baltimore (1996)
    • (1996) Matrix Computations
    • Golub, G.H.1    van Loan, C.F.2
  • 158
    • 3042756404 scopus 로고    scopus 로고
    • Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
    • Grasedyck, L.: Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure. Computing 72, 247–265 (2004)
    • (2004) Computing , vol.72 , Issue.247-265
    • Grasedyck, L.1
  • 159
    • 10044281868 scopus 로고    scopus 로고
    • Existence of a low rank or H-matrix approximant to the solution of a Sylvester equation
    • Grasedyck, L.: Existence of a low rank or H-matrix approximant to the solution of a Sylvester equation. Numer. Linear Algebra Appl. 11, 371–389 (2004)
    • (2004) Numer. Linear Algebra Appl. , vol.11 , pp. 371-389
    • Grasedyck, L.1
  • 160
    • 55749114945 scopus 로고    scopus 로고
    • Nonlinear multigrid for the solution of large-scale Riccati equations in low-rank and H-matrix format
    • Grasedyck, L.: Nonlinear multigrid for the solution of large-scale Riccati equations in low-rank and H-matrix format. Numer. Linear Algebra Appl. 15, 779–807 (2008)
    • (2008) Numer. Linear Algebra Appl. , vol.15 , pp. 779-807
    • Grasedyck, L.1
  • 161
    • 0141829814 scopus 로고    scopus 로고
    • Construction and arithmetics of H-matrices
    • Grasedyck, L., Hackbusch, W.: Construction and arithmetics of H-matrices. Computing 70, 295–334 (2003)
    • (2003) Computing , vol.70 , pp. 295-334
    • Grasedyck, L.1    Hackbusch, W.2
  • 162
    • 48249104699 scopus 로고    scopus 로고
    • A multigrid method to solve large scale Sylvester equations
    • Grasedyck, L., Hackbusch, W.: A multigrid method to solve large scale Sylvester equations. SIAM J. Matrix Anal. Appl. 29, 870–894 (2007)
    • (2007) SIAM J. Matrix Anal. Appl. , vol.29 , pp. 870-894
    • Grasedyck, L.1    Hackbusch, W.2
  • 163
    • 0041340908 scopus 로고    scopus 로고
    • Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
    • Grasedyck, L., Hackbusch, W., Khoromskij, B.: Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Computing 70, 121–165 (2003)
    • (2003) Computing , vol.70 , pp. 121-165
    • Grasedyck, L.1    Hackbusch, W.2    Khoromskij, B.3
  • 165
    • 47849120618 scopus 로고    scopus 로고
    • Parallel black box H-LU preconditioning for elliptic boundary value problems
    • Grasedyck, L., Kriemann, R., Le Borne, S.: Parallel black box H-LU preconditioning for elliptic boundary value problems. Comput. Vis. Sci. 11, 273–291 (2008)
    • (2008) Comput. Vis. Sci. , vol.11 , pp. 273-291
    • Grasedyck, L.1    Kriemann, R.2    Le Borne, S.3
  • 166
    • 67349279102 scopus 로고    scopus 로고
    • Domain decomposition based H-LU pre-conditioning
    • Grasedyck, L., Kriemann, R., Le Borne, S.: Domain decomposition based H-LU pre-conditioning. Numer. Math. 112, 565–600 (2009)
    • (2009) Numer. Math. , vol.112 , pp. 565-600
    • Grasedyck, L.1    Kriemann, R.2    Le Borne, S.3
  • 168
    • 0001610807 scopus 로고
    • Multilevel algorithms considered as iterative methods on semidefinite systems
    • Griebel, M.: Multilevel algorithms considered as iterative methods on semidefinite systems. SIAM J. Sci. Comput. 15, 547–565 (1994)
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 547-565
    • Griebel, M.1
  • 170
    • 21844511143 scopus 로고
    • On the abstract theory of additive and multiplicative Schwarz algorithms
    • Griebel, M., Oswald, P.: On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math. 70, 163–180 (1995)
    • (1995) Numer. Math. , vol.70 , pp. 163-180
    • Griebel, M.1    Oswald, P.2
  • 171
    • 0343071155 scopus 로고
    • The solution of elliptic difference equations by semi-explicit iterative techniques
    • Gunn, J.E.: The solution of elliptic difference equations by semi-explicit iterative techniques. SIAM J. Numer. Anal. 2, 24–45 (1964)
    • (1964) SIAM J. Numer. Anal. , vol.2 , pp. 24-45
    • Gunn, J.E.1
  • 172
    • 0003039594 scopus 로고
    • A class of first order factorization methods
    • Gustafsson, I.: A class of first order factorization methods. BIT 18, 142–156 (1978)
    • (1978) BIT , vol.18 , pp. 142-156
    • Gustafsson, I.1
  • 173
    • 0000497979 scopus 로고
    • A completed theory of the unsymmetric Lanczos process and related algorithms, part I
    • Gutknecht, M.H.: A completed theory of the unsymmetric Lanczos process and related algorithms, part I. SIAM J. Matrix Anal. Appl. 13, 594–639 (1992)
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 594-639
    • Gutknecht, M.H.1
  • 174
    • 0009165708 scopus 로고
    • A completed theory of the unsymmetric Lanczos process and related algorithms, part II
    • Gutknecht, M.H.: A completed theory of the unsymmetric Lanczos process and related algorithms, part II. SIAM J. Matrix Anal. Appl. 15, 15–58 (1994)
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 15-58
    • Gutknecht, M.H.1
  • 175
    • 85011492167 scopus 로고    scopus 로고
    • Lanczos-type solvers for nonsymmetric linear systems of equations
    • Gutknecht, M.H.: Lanczos-type solvers for nonsymmetric linear systems of equations. Acta Numerica 6, 271–397 (1997)
    • (1997) Acta Numerica , vol.6 , pp. 271-397
    • Gutknecht, M.H.1
  • 177
    • 77958413026 scopus 로고
    • The fast numerical solution of very large elliptic difference schemes
    • Hackbusch, W.: The fast numerical solution of very large elliptic difference schemes. J. Inst. Maths. Appl. 26, 119–132 (1980)
    • (1980) J. Inst. Maths. Appl. , vol.26 , pp. 119-132
    • Hackbusch, W.1
  • 178
    • 84862307911 scopus 로고
    • Bemerkungen zur iterativen Defektkorrektur und zu ihrer Kombination mit Mehrgitterverfahren
    • Hackbusch, W.: Bemerkungen zur iterativen Defektkorrektur und zu ihrer Kombination mit Mehrgitterverfahren. Rev. Roumaine Math. Pures Appl. 26, 1319–1329 (1981)
    • (1981) Rev. Roumaine Math. Pures Appl. , vol.26 , pp. 1319-1329
    • Hackbusch, W.1
  • 179
    • 0042755616 scopus 로고
    • Fast numerical solution of time-periodic parabolic problems by a multi-grid method
    • Hackbusch, W.: Fast numerical solution of time-periodic parabolic problems by a multi-grid method. SIAM J. Sci. Statist. Comput. 2, 198–206 (1981)
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 198-206
    • Hackbusch, W.1
  • 180
    • 1542451509 scopus 로고
    • On the regularity of difference schemes
    • Hackbusch, W.: On the regularity of difference schemes. Ark. Mat. 19, 71–95 (1981)
    • (1981) Ark. Mat. , vol.19 , pp. 71-95
    • Hackbusch, W.1
  • 181
    • 33746359794 scopus 로고
    • On the regularity of difference schemes, part II: Regularity estimates for linear and nonlinear problems
    • Hackbusch, W.: On the regularity of difference schemes, part II: regularity estimates for linear and nonlinear problems. Ark. Mat. 21, 3–28 (1983)
    • (1983) Ark. Mat. , vol.21 , pp. 3-28
    • Hackbusch, W.1
  • 184
    • 85067970307 scopus 로고    scopus 로고
    • Multi-grid methods of the second kind
    • ], pp
    • Hackbusch, W.: Multi-grid methods of the second kind. In: Paddon and Holstein [306], pp. 11–83
    • Paddon and Holstein , vol.306 , pp. 11-83
    • Hackbusch, W.1
  • 185
    • 85067935646 scopus 로고
    • Robust Multi-grid Methods, Notes on Numerical Fluid Mechanics, Vol. 23. Vieweg, Braunschweig (1988)
    • (ed.), Jan
    • Hackbusch, W. (ed.): Robust Multi-grid Methods, Notes on Numerical Fluid Mechanics, Vol. 23. Vieweg, Braunschweig (1988). (Kiel, Jan. 1988)
    • (1988) (Kiel
    • Hackbusch, W.1
  • 186
    • 34249963996 scopus 로고
    • The frequency decomposition multi-grid method, part I: Application to anisotropic equations
    • Hackbusch, W.: The frequency decomposition multi-grid method, part I: application to anisotropic equations. Numer. Math. 56, 229–245 (1989)
    • (1989) Numer. Math. , vol.56 , pp. 229-245
    • Hackbusch, W.1
  • 187
    • 85067918128 scopus 로고
    • Parallel algorithms for PDEs, Notes on Numerical Fluid Mechanics, Vol. 31. Vieweg, Braunschweig (1991)
    • (ed.), Jan
    • Hackbusch, W. (ed.): Parallel algorithms for PDEs, Notes on Numerical Fluid Mechanics, Vol. 31. Vieweg, Braunschweig (1991). (Kiel, Jan. 1990)
    • (1990) (Kiel
    • Hackbusch, W.1
  • 188
    • 0039829375 scopus 로고
    • The solution of large systems of BEM equations by the multi-grid and panel clustering technique
    • pp
    • Hackbusch, W.: The solution of large systems of BEM equations by the multi-grid and panel clustering technique. Rend. Semin. Mat. Politec. Torino pp. 163–187 (1991)
    • (1991) Rend. Semin. Mat. Politec. Torino , pp. 163-187
    • Hackbusch, W.1
  • 189
    • 84983967473 scopus 로고
    • Comparison of different multi-grid variants for nonlinear equations
    • Hackbusch, W.: Comparison of different multi-grid variants for nonlinear equations. ZAMM 72, 148–151 (1992)
    • (1992) ZAMM , vol.72 , pp. 148-151
    • Hackbusch, W.1
  • 190
    • 21144473803 scopus 로고
    • The frequency decomposition multi-grid method, part II: Convergence analysis based on the additive Schwarz method
    • Hackbusch, W.: The frequency decomposition multi-grid method, part II: convergence analysis based on the additive Schwarz method. Numer. Math. 63, 433–453 (1992)
    • (1992) Numer. Math. , vol.63 , pp. 433-453
    • Hackbusch, W.1
  • 192
    • 85067998132 scopus 로고    scopus 로고
    • Hackbusch, W.: Direct domain decomposition using the hierarchical matrix technique. In: Herrera et al. [217], pp. 39–50
    • Hackbusch, W.1
  • 196
    • 84900490000 scopus 로고    scopus 로고
    • Numerical tensor calculus
    • Hackbusch, W.: Numerical tensor calculus. Acta Numerica 23, 651–742 (2014)
    • (2014) Acta Numerica , vol.23 , pp. 651-742
    • Hackbusch, W.1
  • 199
    • 84955727396 scopus 로고    scopus 로고
    • Solution of linear systems in high spatial dimensions
    • Hackbusch, W.: Solution of linear systems in high spatial dimensions. Comput. Vis. Sci. 17, 111–118 (2015).
    • (2015) Comput. Vis. Sci. , vol.17 , pp. 111-118
    • Hackbusch, W.1
  • 200
    • 84954403869 scopus 로고    scopus 로고
    • New estimates for the recursive low-rank truncation of block-structured matrices
    • Hackbusch, W.: New estimates for the recursive low-rank truncation of block-structured matrices. Numer. Math. 132, 303–328 (2016).
    • (2016) Numer. Math. , vol.132 , pp. 303-328
    • Hackbusch, W.1
  • 202
    • 29044447358 scopus 로고    scopus 로고
    • Direct Schur complement method by domain decomposition based on H-matrix approximation
    • Hackbusch, W., Khoromskij, B., Kriemann, R.: Direct Schur complement method by domain decomposition based on H-matrix approximation. Comput. Vis. Sci. 8, 179–188 (2005)
    • (2005) Comput. Vis. Sci. , vol.8 , pp. 179-188
    • Hackbusch, W.1    Khoromskij, B.2    Kriemann, R.3
  • 204
    • 0001654023 scopus 로고
    • Analysis of a damped nonlinear multilevel method
    • Hackbusch, W., Reusken, A.: Analysis of a damped nonlinear multilevel method. Numer. Math. 55, 225–246 (1989)
    • (1989) Numer. Math. , vol.55 , pp. 225-246
    • Hackbusch, W.1    Reusken, A.2
  • 205
    • 85067999625 scopus 로고
    • Multigrid Methods, Lect. Notes Math., Vol. 960. Springer, Berlin (1982)
    • (eds.), Nov
    • Hackbusch, W., Trottenberg, U. (eds.): Multigrid Methods, Lect. Notes Math., Vol. 960. Springer, Berlin (1982). (Köln-Porz, Nov. 1981)
    • (1981) (Köln-Porz
    • Hackbusch, W.1    Trottenberg, U.2
  • 206
    • 85067950679 scopus 로고
    • Multigrid Methods II, Lect. Notes Math., Vol. 1228. Springer, Berlin (1986)
    • (eds.), Oct
    • Hackbusch, W., Trottenberg, U. (eds.): Multigrid Methods II, Lect. Notes Math., Vol. 1228. Springer, Berlin (1986). (Köln, Oct. 1985)
    • (1985) (Köln
    • Hackbusch, W.1    Trottenberg, U.2
  • 207
    • 85067956447 scopus 로고
    • Multigrid Methods III, ISNM, Vol. 98. Birkhäuser, Basel (1991)
    • (eds.), Oct
    • Hackbusch, W., Trottenberg, U. (eds.): Multigrid Methods III, ISNM, Vol. 98. Birkhäuser, Basel (1991). (Bonn, Oct. 1990)
    • (1990) (Bonn
    • Hackbusch, W.1    Trottenberg, U.2
  • 208
    • 85068013825 scopus 로고
    • Incomplete Decompositions (ILU) – Algorithms, Theory, and Applications, Notes on Numerical Fluid Mechanics, Vol. 41. Vieweg, Braunschweig (1992)
    • (eds.), Jan
    • Hackbusch, W., Wittum, G. (eds.): Incomplete Decompositions (ILU) – Algorithms, Theory, and Applications, Notes on Numerical Fluid Mechanics, Vol. 41. Vieweg, Braunschweig (1992). (Kiel, Jan. 1992)
    • (1992) (Kiel
    • Hackbusch, W.1    Wittum, G.2
  • 209
    • 85068009831 scopus 로고
    • Fast Solvers for Flow Problems, Notes on Numerical Fluid Mechanics, Vol. 49. Vieweg, Braunschweig (1995)
    • (eds.), Jan
    • Hackbusch, W., Wittum, G. (eds.): Fast Solvers for Flow Problems, Notes on Numerical Fluid Mechanics, Vol. 49. Vieweg, Braunschweig (1995). (Kiel, Jan. 1994)
    • (1994) (Kiel
    • Hackbusch, W.1    Wittum, G.2
  • 211
    • 0034323048 scopus 로고    scopus 로고
    • Successive overrelaxation (SOR) and related methods
    • Hadjidimos, A.: Successive overrelaxation (SOR) and related methods. J. Comput. Appl. Math. 123, 177–199 (2000)
    • (2000) J. Comput. Appl. Math. , vol.123 , pp. 177-199
    • Hadjidimos, A.1
  • 213
    • 44949277442 scopus 로고
    • On the SOR method for symmetric positive definite systems
    • Hanke, M., Neumann, M., Niethammer, W.: On the SOR method for symmetric positive definite systems. Linear Algebra Appl. 154, 457–472 (1991)
    • (1991) Linear Algebra Appl , vol.154 , pp. 457-472
    • Hanke, M.1    Neumann, M.2    Niethammer, W.3
  • 214
    • 0001424792 scopus 로고
    • Tensor rank is NP-complete
    • Håstad, J.: Tensor rank is NP-complete. J. Algorithms 11, 644–654 (1990)
    • (1990) J. Algorithms , vol.11 , pp. 644-654
    • Håstad, J.1
  • 215
    • 0021510651 scopus 로고
    • Gauss and the history of the fast Fourier transform
    • Heideman, M.T., Johnson, D.H., Burrus, C.S.: Gauss and the history of the fast Fourier transform. IEEE ASSP Magazine 1(4), 14–21 (1984)
    • (1984) IEEE ASSP Magazine , vol.1 , Issue.4 , pp. 14-21
    • Heideman, M.T.1    Johnson, D.H.2    Burrus, C.S.3
  • 216
    • 85067976668 scopus 로고
    • Multigrid Methods IV, ISNM, Vol. 116. Birkhäuser
    • (eds.), Amsterdam, July
    • Hemker, P.W., Wesseling, P. (eds.): Multigrid Methods IV, ISNM, Vol. 116. Birkhäuser, Basel (1994). (Amsterdam, July 1993)
    • (1993) Basel , vol.1994
    • Hemker, P.W.1    Wesseling, P.2
  • 217
    • 85068007252 scopus 로고    scopus 로고
    • Domain Decomposition Methods in Science and Engineering. National Autonomous University of Mexico
    • (eds.), Cocoyoc, Mexico, Jan
    • Herrera, I., Keyes, D.E., Widlund, O.B., Yates, R. (eds.): Domain Decomposition Methods in Science and Engineering. National Autonomous University of Mexico, Mexico City (2003). (Cocoyoc, Mexico, Jan. 2002)
    • (2002) Mexico City , vol.2003
    • Herrera, I.1    Keyes, D.E.2    Widlund, O.B.3    Yates, R.4
  • 219
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49, 409–436 (1952)
    • (1952) J. Res. Nat. Bur. Standards , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 220
    • 0040958621 scopus 로고
    • Neue Methoden zur approximativen Integration der Differentialgleichungen einer unabhängigen Veränderlichen
    • Heun, K.: Neue Methoden zur approximativen Integration der Differentialgleichungen einer unabhängigen Veränderlichen. Z. für Math. und Phys. 45, 23–38 (1900)
    • (1900) Z. für Math. Und Phys. , vol.45 , pp. 23-38
    • Heun, K.1
  • 223
    • 84932220767 scopus 로고
    • A fast direct solution of Poisson’s equation using Fourier analysis
    • Hockney, R.W.: A fast direct solution of Poisson’s equation using Fourier analysis. J. ACM 12, 95–113 (1965)
    • (1965) J. ACM , vol.12 , pp. 95-113
    • Hockney, R.W.1
  • 224
    • 84861379430 scopus 로고    scopus 로고
    • The alternating linear scheme for tensor optimization in the tensor train format
    • Holtz, S., Rohwedder, T., Schneider, R.: The alternating linear scheme for tensor optimization in the tensor train format. SIAM J. Sci. Comput. 34, A683–A713 (2012)
    • (2012) SIAM J. Sci. Comput. , vol.34 , pp. A683-A713
    • Holtz, S.1    Rohwedder, T.2    Schneider, R.3
  • 226
    • 0039115417 scopus 로고
    • Somes estimates for conjugate gradient methods
    • Ilin, V.P.: Somes estimates for conjugate gradient methods. USSR Comput. Math. Math. Phys. 16,4, 22–30 (1976)
    • (1976) USSR Comput. Math. Math. Phys. , vol.16 , Issue.4 , pp. 22-30
    • Ilin, V.P.1
  • 227
    • 0000237258 scopus 로고
    • Über eine neue Auflösungsart der bei der Methode der kleinsten Quadrate vorkommenden linearen Gleichungen
    • Jacobi, C.G.J.: Über eine neue Auflösungsart der bei der Methode der kleinsten Quadrate vorkommenden linearen Gleichungen. Astron. Nachr. 32, 297–306 (1845)
    • (1845) Astron. Nachr. , vol.32 , pp. 297-306
    • Jacobi, C.G.J.1
  • 228
    • 0040361018 scopus 로고
    • Partial elimination
    • Jennings, A., Malik, G.M.: Partial elimination. J. IMA 20, 307–316 (1977)
    • (1977) J. IMA , vol.20 , pp. 307-316
    • Jennings, A.1    Malik, G.M.2
  • 231
    • 0042506433 scopus 로고
    • Approximate solution of systems of linear equations
    • Kaczmarz, S.: Approximate solution of systems of linear equations. Internat. J. Control 57, 1269–1271 (1993)
    • (1993) Internat. J. Control , vol.57 , pp. 1269-1271
    • Kaczmarz, S.1
  • 232
    • 0039337489 scopus 로고
    • Gauss–Seidel methods of solving large systems of linear equations. Doctoral thesis
    • Kahan, W.M.: Gauss–Seidel methods of solving large systems of linear equations. Doctoral thesis, University of Toronto, Canada (1958)
    • (1958) Canada
    • Kahan, W.M.1
  • 235
    • 0000876881 scopus 로고    scopus 로고
    • Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods
    • pp
    • Kettler, R.: Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods. In: Hackbusch and Trottenberg [205], pp. 502–534
    • Hackbusch and Trottenberg [205] , pp. 502-534
    • Kettler, R.1
  • 236
    • 85067929704 scopus 로고
    • Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM
    • (eds.), Norfolk, May
    • Keyes, D.E., Chan, T.F., Meurant, G.A., Scroggs, J.S., Voigt, R.G. (eds.): Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia (1992). (Norfolk, May 1991)
    • (1991) Philadelphia , vol.1992
    • Keyes, D.E.1    Chan, T.F.2    Meurant, G.A.3    Scroggs, J.S.4    Voigt, R.G.5
  • 237
    • 85067968430 scopus 로고
    • Domain Decomposition Methods in Science and Engineering Computing. AMS
    • (eds.), Penn State, Oct
    • Keyes, D.E., Xu, J. (eds.): Domain Decomposition Methods in Science and Engineering Computing. AMS, Providence (1994). (Penn State, Oct. 1993)
    • (1993) Providence , vol.1994
    • Keyes, D.E.1    Xu, J.2
  • 241
    • 84950009115 scopus 로고
    • The limit points of affine iterations
    • Kosmol, P., Zhou, X.: The limit points of affine iterations. Numer. Funct. Anal. Optim. 11, 403–409 (1990)
    • (1990) Numer. Funct. Anal. Optim. , vol.11 , pp. 403-409
    • Kosmol, P.1    Zhou, X.2
  • 242
    • 77956045829 scopus 로고    scopus 로고
    • Krylov subspace methods for linear systems with tensor product structure
    • Kressner, D., Tobler, C.: Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl. 31, 1688–1714 (2010)
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 1688-1714
    • Kressner, D.1    Tobler, C.2
  • 243
    • 84856290662 scopus 로고    scopus 로고
    • Low-rank tensor Krylov subspace methods for parametrized linear systems
    • Kressner, D., Tobler, C.: Low-rank tensor Krylov subspace methods for parametrized linear systems. SIAM J. Matrix Anal. Appl. 32, 1288–1316 (2011)
    • (2011) SIAM J. Matrix Anal. Appl. , vol.32 , pp. 1288-1316
    • Kressner, D.1    Tobler, C.2
  • 244
    • 80053926097 scopus 로고    scopus 로고
    • Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems
    • Kressner, D., Tobler, C.: Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems. Comput. Methods Appl. Math. 11, 363–381 (2011)
    • (2011) Comput. Methods Appl. Math. , vol.11 , Issue.363-381
    • Kressner, D.1    Tobler, C.2
  • 245
    • 18844419238 scopus 로고    scopus 로고
    • Parallel H-matrix arithmetics on shared memory systems
    • Kriemann, R.: Parallel H-matrix arithmetics on shared memory systems. Computing 74, 273–297 (2005)
    • (2005) Computing , vol.74 , pp. 273-297
    • Kriemann, R.1
  • 246
    • 84955752798 scopus 로고    scopus 로고
    • H-FAINV: Hierarchically factored approximate inverse pre-conditioners
    • Kriemann, R., Le Borne, S.: H-FAINV: hierarchically factored approximate inverse pre-conditioners. Comput. Vis. Sci. 17, 135–150 (2015).
    • (2015) Comput. Vis. Sci. , vol.17 , pp. 135-150
    • Kriemann, R.1    Le Borne, S.2
  • 247
    • 34250407909 scopus 로고
    • A note on the ‘nested iteration’ method
    • Kronsjö, L.: A note on the ‘nested iteration’ method. BIT 15, 107–110 (1975)
    • (1975) BIT , vol.15 , pp. 107-110
    • Kronsjö, L.1
  • 248
    • 3643135186 scopus 로고
    • Kronsjö, L., Dahlquist, G.: On the design of nested iterations for elliptic difference equations. BIT 12, 63–71 (1972). [The front page of the paper shows wrong data: vol. 11 (1971)]
    • (1972)
    • Kronsjö, L.1    Dahlquist, G.2
  • 249
    • 0347108088 scopus 로고
    • On the numerical solution of the equation by which in technical questions frequencies of small oscillations of material systems are determined [in Russian]
    • Krylov, A. N.: On the numerical solution of the equation by which in technical questions frequencies of small oscillations of material systems are determined [in Russian]. Izvestiya Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk 7, 491–539 (1931)
    • (1931) Izvestiya Akademii Nauk SSSR, Otdelenie Matematicheskikh I Estestvennykh Nauk , vol.7 , pp. 491-539
    • Krylov, A.N.1
  • 250
    • 0006451452 scopus 로고
    • Beitrag zur näherungsweisen Integration totaler Differentialgleichungen
    • Kutta, W. M.: Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Zeitschrift für Math. und Phys. 46, 435–453 (1901)
    • (1901) Zeitschrift für Math. Und Phys. , vol.46 , pp. 435-453
    • Kutta, W.M.1
  • 252
    • 0024750686 scopus 로고
    • Multigrid domain decomposition methods for elliptic problems
    • Kuznetsov, Y.A.: Multigrid domain decomposition methods for elliptic problems. Comput. Methods Appl. Mech. Engrg. 75, 185–193 (1989)
    • (1989) Comput. Methods Appl. Mech. Engrg. , vol.75 , pp. 185-193
    • Kuznetsov, Y.A.1
  • 254
    • 85068004603 scopus 로고    scopus 로고
    • Eleventh International Conference on Domain Decomposition Methods
    • (eds.), Greenwich, July
    • Lai, C.H., Bjørstad, P.E., Cross, M., Widlund, O.B. (eds.): Eleventh International Conference on Domain Decomposition Methods. ddm.org (1999). (Greenwich, July 1998)
    • (1998) Ddm.Org , vol.1999
    • Lai, C.H.1    Bjørstad, P.E.2    Cross, M.3    Widlund, O.B.4
  • 255
    • 0002814189 scopus 로고
    • Solution of systems of linear equations by minimized iterations
    • Lanczos, C.: Solution of systems of linear equations by minimized iterations. J. Res. Nat. Bur. Standards 49, 33–53 (1952)
    • (1952) J. Res. Nat. Bur. Standards , vol.49 , pp. 33-53
    • Lanczos, C.1
  • 256
    • 0000518587 scopus 로고
    • An iteration formula for Fredholm integral equations of the first kind
    • Landweber, L.: An iteration formula for Fredholm integral equations of the first kind. Amer. J. Math. 73, 615–624 (1951)
    • (1951) Amer. J. Math. , vol.73 , pp. 615-624
    • Landweber, L.1
  • 257
    • 85067974518 scopus 로고
    • Boundary Problems in Differential Equations. Kluwer Academic Publ
    • (ed.), Madison, April
    • Langer, R.E. (ed.): Boundary Problems in Differential Equations. Kluwer Academic Publ., Dortrecht (1960). (Madison, April 1959)
    • (1959) Dortrecht , vol.1960
    • Langer, R.E.1
  • 259
    • 37249041765 scopus 로고    scopus 로고
    • Domain decomposition based H-LU precondi-tioners
    • pp., New York, Jan
    • Le Borne, S., Grasedyck, L., Kriemann, R.: Domain decomposition based H-LU precondi-tioners. In: Widlund and Keyes [399], pp. 661–668. (New York, Jan. 2005)
    • (2005) Widlund and Keyes [399] , pp. 661-668
    • Le Borne, S.1    Grasedyck, L.2    Kriemann, R.3
  • 260
    • 49349134504 scopus 로고
    • On a Zolotarev problem in the method of alternating directions
    • Lebedev, V.I.: On a Zolotarev problem in the method of alternating directions. USSR Comput. Math. Math. Phys. 17,2, 58–76 (1971)
    • (1971) USSR Comput. Math. Math. Phys. , vol.17 , Issue.2 , pp. 58-76
    • Lebedev, V.I.1
  • 261
    • 49649149429 scopus 로고
    • On the order of choice of the iteration parameters in the Chebyshev cyclic iteration method
    • Lebedev, V.I., Finogenov, S.A.: On the order of choice of the iteration parameters in the Chebyshev cyclic iteration method. USSR Comput. Math. Math. Phys. 11,2, 155–170 (1971)
    • (1971) USSR Comput. Math. Math. Phys. , vol.11 , Issue.2 , pp. 155-170
    • Lebedev, V.I.1    Finogenov, S.A.2
  • 262
    • 0007945322 scopus 로고
    • On the order of choice of the iteration parameters in the Chebyshev cyclic iteration method
    • Lebedev, V.I., Finogenov, S.A.: On the order of choice of the iteration parameters in the Chebyshev cyclic iteration method. USSR Comput. Math. Math. Phys. 13,1, 21–41 (1973)
    • (1973) USSR Comput. Math. Math. Phys. , vol.13 , Issue.1 , pp. 21-41
    • Lebedev, V.I.1    Finogenov, S.A.2
  • 264
    • 20044365008 scopus 로고    scopus 로고
    • Orthogonal Hessenberg reduction and orthogonal Krylov subspace bases
    • Liesen, J., Saylor, P.E.: Orthogonal Hessenberg reduction and orthogonal Krylov subspace bases. SIAM J. Numer. Anal. 42, 2148–2158 (2005)
    • (2005) SIAM J. Numer. Anal. , vol.42 , pp. 2148-2158
    • Liesen, J.1    Saylor, P.E.2
  • 266
    • 85067936160 scopus 로고    scopus 로고
    • Lions, P. L.: On the Schwarz alternating method I. In: Glowinski et al. [150], pp. 1–42
    • Lions, P.L.1
  • 268
    • 55549120903 scopus 로고    scopus 로고
    • Algebraic multigrid solvers for complex-valued matrices
    • MacLachlan, S.P., Oosterlee, C.W.: Algebraic multigrid solvers for complex-valued matrices. SIAM J. Sci. Comput. 30, 1548–1571 (2008)
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1548-1571
    • Maclachlan, S.P.1    Oosterlee, C.W.2
  • 269
    • 0021374981 scopus 로고
    • A multilevel iterative method for symmetric, positive definite problems
    • Mandel, J.L.: A multilevel iterative method for symmetric, positive definite problems. Appl. Math. Optim. 11, 77–95 (1984)
    • (1984) Appl. Math. Optim. , vol.11 , pp. 77-95
    • Mandel, J.L.1
  • 270
    • 0002068824 scopus 로고
    • On block diagonal and Schur complement preconditioning
    • Mandel, J.L.: On block diagonal and Schur complement preconditioning. Numer. Math. 58, 79–93 (1990)
    • (1990) Numer. Math. , vol.58 , pp. 79-93
    • Mandel, J.L.1
  • 271
    • 85067945075 scopus 로고    scopus 로고
    • The Tenth International Conference on Domain Decomposition Methods. AMS
    • (ed.), Boulder, Aug
    • Mandel, J.L. (ed.): The Tenth International Conference on Domain Decomposition Methods. AMS, Providence (1998). (Boulder, Aug. 1997)
    • (1997) Providence , vol.1998
    • Mandel, J.L.1
  • 272
    • 34250261642 scopus 로고
    • Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration
    • Manteuffel, T.A.: Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration. Numer. Math. 31, 183–208 (1978)
    • (1978) Numer. Math. , vol.31 , pp. 183-208
    • Manteuffel, T.A.1
  • 273
    • 84966241510 scopus 로고
    • An incomplete factorization technique for positive definite linear systems
    • Manteuffel, T.A.: An incomplete factorization technique for positive definite linear systems. Math. Comp. 34, 473–497 (1980)
    • (1980) Math. Comp. , vol.34 , pp. 473-497
    • Manteuffel, T.A.1
  • 274
    • 70350504025 scopus 로고    scopus 로고
    • Splitting and alternating direction methods
    • ], pp
    • Marchuk, G.: Splitting and alternating direction methods. In: Ciarlet–Lions [96], pp. 197–462
    • Ciarlet–Lions [96 , pp. 197-462
    • Marchuk, G.1
  • 277
    • 84858793640 scopus 로고    scopus 로고
    • Solving stochastic systems with low-rank tensor compression
    • Matthies, H.G., Zander, E.: Solving stochastic systems with low-rank tensor compression. Linear Algebra Appl. 436, 3819–3838 (2012)
    • (2012) Linear Algebra Appl , vol.436 , pp. 3819-3838
    • Matthies, H.G.1    Zander, E.2
  • 278
    • 0004252812 scopus 로고
    • McCormick, S.F. (ed.), SIAM, Philadelphia
    • McCormick, S.F. (ed.): Multigrid Methods. SIAM, Philadelphia (1987)
    • (1987) Multigrid Methods
  • 279
    • 0020907504 scopus 로고    scopus 로고
    • Iterative methods for the solution of linear equations based on incomplete factorisation of the matrix. Shell Publ. 643, Rijswijk (1983)
    • Meijerink, J.: Iterative methods for the solution of linear equations based on incomplete factorisation of the matrix. Shell Publ. 643, Rijswijk (1983). Published as SPE Conference Paper, doi:10.2118/12262-MS
    • Published as SPE Conference Paper
    • Meijerink, J.1
  • 280
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • Meijerink, J., van der Vorst, H.A.: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp. 31, 148–162 (1977)
    • (1977) Math. Comp. , vol.31 , pp. 148-162
    • Meijerink, J.1    van der Vorst, H.A.2
  • 284
    • 84869406121 scopus 로고    scopus 로고
    • Musings on multilinear fitting
    • Mohlenkamp, M.J.: Musings on multilinear fitting. Linear Algebra Appl. 438, 834–852 (2013)
    • (2013) Linear Algebra Appl , vol.438 , pp. 834-852
    • Mohlenkamp, M.J.1
  • 286
    • 30244517736 scopus 로고
    • Domain decomposition method for elliptic mixed boundary value problems
    • Mróz, M.: Domain decomposition method for elliptic mixed boundary value problems. Computing 42, 45–59 (1989)
    • (1989) Computing , vol.42 , pp. 45-59
    • Mróz, M.1
  • 289
    • 0041116669 scopus 로고
    • Exact convergence and divergence domains for the symmetric successive overrelaxation iterative (SSOR) method applied to H-matrices
    • Neumaier, A., Varga, R.S.: Exact convergence and divergence domains for the symmetric successive overrelaxation iterative (SSOR) method applied to H-matrices. Linear Algebra Appl. 58, 261–272 (1984)
    • (1984) Linear Algebra Appl , vol.58 , pp. 261-272
    • Neumaier, A.1    Varga, R.S.2
  • 290
    • 0040234132 scopus 로고
    • On multiple grid and related techniques for solving discrete elliptic systems
    • Nicolaides, R.: On multiple grid and related techniques for solving discrete elliptic systems. J. Comput. Phys. 19, 418–431 (1975)
    • (1975) J. Comput. Phys. , vol.19 , pp. 418-431
    • Nicolaides, R.1
  • 291
    • 34250955507 scopus 로고
    • Relaxation bei komplexen Matrizen
    • Niethammer, W.: Relaxation bei komplexen Matrizen. Math. Z. 86, 34–40 (1964)
    • (1964) Math. Z. , vol.86 , pp. 34-40
    • Niethammer, W.1
  • 292
    • 0008327883 scopus 로고
    • Relaxation bei nichtsymmetrischen Matrizen
    • Niethammer, W.: Relaxation bei nichtsymmetrischen Matrizen. Math. Z. 85, 319–327 (1964)
    • (1964) Math. Z. , vol.85 , pp. 319-327
    • Niethammer, W.1
  • 293
    • 0343922107 scopus 로고
    • The SOR method on parallel computers
    • Niethammer, W.: The SOR method on parallel computers. Numer. Math. 56, 247–254 (1989)
    • (1989) Numer. Math. , vol.56 , pp. 247-254
    • Niethammer, W.1
  • 294
    • 0007994014 scopus 로고
    • The analysis of k-step iterative methods for linear systems from summability theory
    • Niethammer, W., Varga, R.S.: The analysis of k-step iterative methods for linear systems from summability theory. Numer. Math. 41, 177–206 (1983)
    • (1983) Numer. Math. , vol.41 , pp. 177-206
    • Niethammer, W.1    Varga, R.S.2
  • 295
    • 84962009622 scopus 로고    scopus 로고
    • Multigrid with ILU-smoothing: Systematic tests and improvements
    • ], pp
    • Oertel, K.D., Stüben, K.: Multigrid with ILU-smoothing: systematic tests and improvements. In: Hackbusch [185], pp. 188–199
    • Hackbusch [185 , pp. 188-199
    • Oertel, K.D.1    Stüben, K.2
  • 296
    • 0001324833 scopus 로고
    • Multi-splitting of matrices and parallel solution of linear systems
    • O’Leary, D.P., White, R.E.: Multi-splitting of matrices and parallel solution of linear systems. SIAM J. Alg. Disc. Meth. 6, 630–640 (1985)
    • (1985) SIAM J. Alg. Disc. Meth. , vol.6 , pp. 630-640
    • O’Leary, D.P.1    White, R.E.2
  • 297
    • 0007425964 scopus 로고
    • Richardson’s iteration for nonsymmetric matrices
    • Opfer, G., Schober, G.: Richardson’s iteration for nonsymmetric matrices. Linear Algebra Appl. 58, 343–361 (1984)
    • (1984) Linear Algebra Appl , vol.58 , pp. 343-361
    • Opfer, G.1    Schober, G.2
  • 299
    • 80053929473 scopus 로고    scopus 로고
    • DMRG approach to fast linear algebra in the TT-format
    • Oseledets, I.V.: DMRG approach to fast linear algebra in the TT-format. Comput. Methods Appl. Math. 11, 382–393 (2011)
    • (2011) Comput. Methods Appl. Math. , vol.11 , Issue.382-393
    • Oseledets, I.V.1
  • 300
    • 70449525345 scopus 로고    scopus 로고
    • TT-cross approximation for multidimensional arrays
    • Oseledets, I.V., Tyrtyshnikov, E.E.: TT-cross approximation for multidimensional arrays. Linear Algebra Appl. 432, 70–88 (2010)
    • (2010) Linear Algebra Appl , vol.432 , pp. 70-88
    • Oseledets, I.V.1    Tyrtyshnikov, E.E.2
  • 301
    • 13544261154 scopus 로고
    • Über die Determinanten mit überwiegender Hauptdiagonale
    • Ostrowski, A.M.: Über die Determinanten mit überwiegender Hauptdiagonale. Comment. Math. Helv. 10, 69–96 (1937)
    • (1937) Comment. Math. Helv. , vol.10 , pp. 69-96
    • Ostrowski, A.M.1
  • 302
    • 0005653333 scopus 로고
    • On the linear iteration procedures for symmetric matrices
    • Ostrowski, A.M.: On the linear iteration procedures for symmetric matrices. Rend. Math. Appl. 14, 140–163 (1954)
    • (1954) Rend. Math. Appl. , vol.14 , pp. 140-163
    • Ostrowski, A.M.1
  • 303
    • 0001988435 scopus 로고
    • On function spaces related to finite element approximation theory
    • Oswald, P.: On function spaces related to finite element approximation theory. Z. Anal. Anwendungen 9, 43–64 (1990)
    • (1990) Z. Anal. Anwendungen , vol.9 , pp. 43-64
    • Oswald, P.1
  • 305
    • 0028729679 scopus 로고
    • On the convergence rate of SOR: A worst case estimate
    • Oswald, P.: On the convergence rate of SOR: a worst case estimate. Computing 52, 245–255 (1994)
    • (1994) Computing , vol.52 , pp. 245-255
    • Oswald, P.1
  • 306
    • 85067917284 scopus 로고
    • Multigrid Methods for Integral and Differential Equations. Clarendon Press
    • (eds.), Bristol, Sep
    • Paddon, D.J., Holstein, H. (eds.): Multigrid Methods for Integral and Differential Equations. Clarendon Press, Oxford (1985). (Bristol, Sep. 1983)
    • (1983) Oxford , vol.1985
    • Paddon, D.J.1    Holstein, H.2
  • 307
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12, 617–629 (1975)
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 308
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • Peaceman, D.W., Rachford, H.H.: The numerical solution of parabolic and elliptic differential equations. J. SIAM 3, 28–41 (1955)
    • (1955) J. SIAM , vol.3 , pp. 28-41
    • Peaceman, D.W.1    Rachford, H.H.2
  • 309
    • 0008515048 scopus 로고
    • An elementary proof of the power inequality for the numerical radius
    • Pearcy, C.: An elementary proof of the power inequality for the numerical radius. Michigan Math. J. 13, 289–291 (1966)
    • (1966) Michigan Math. J. , vol.13 , pp. 289-291
    • Pearcy, C.1
  • 310
    • 0001082478 scopus 로고    scopus 로고
    • Low rank solution of data-sparse Sylvester equations
    • Penzl, T.: Low rank solution of data-sparse Sylvester equations. Systems Control Lett. 40, 139–144 (2000)
    • (2000) Systems Control Lett , vol.40 , pp. 139-144
    • Penzl, T.1
  • 311
    • 0000790899 scopus 로고
    • Zur Theorie der Matrices
    • Perron, O.: Zur Theorie der Matrices. Math. Ann. 64, 248–263 (1907)
    • (1907) Math. Ann. , vol.64 , pp. 248-263
    • Perron, O.1
  • 312
    • 84966208957 scopus 로고
    • On the numerical solution of Helmholtz’s equation by the capacitance matrix method
    • Proskurowski, W., Widlund, O.B.: On the numerical solution of Helmholtz’s equation by the capacitance matrix method. Math. Comp. 30, 433–468 (1976)
    • (1976) Math. Comp. , vol.30 , pp. 433-468
    • Proskurowski, W.1    Widlund, O.B.2
  • 313
    • 85067932311 scopus 로고
    • Domain Decomposition Methods in Science and Engineering. AMS, Providence (1994)
    • (eds.), Jun
    • Quarteroni, A., Périaux, J., Kuznetsov, Y.A., Widlund, O.B. (eds.): Domain Decomposition Methods in Science and Engineering. AMS, Providence (1994). (Como, Jun. 1992)
    • (1992) (Como
    • Quarteroni, A.1    Périaux, J.2    Kuznetsov, Y.A.3    Widlund, O.B.4
  • 316
    • 0039879187 scopus 로고
    • On the convergence of the classical iterative procedures for symmetric matrices
    • Reich, E.: On the convergence of the classical iterative procedures for symmetric matrices. Ann. Math. Statist. 20, 448–451 (1949)
    • (1949) Ann. Math. Statist. , vol.20 , pp. 448-451
    • Reich, E.1
  • 317
    • 84910798790 scopus 로고
    • A method for finding the optimum successive overrelaxation factor
    • Reid, J.K.: A method for finding the optimum successive overrelaxation factor. Comput. J. 9, 200–204 (1966)
    • (1966) Comput. J. , vol.9 , pp. 200-204
    • Reid, J.K.1
  • 318
    • 85067962580 scopus 로고
    • Large Sparse Sets of Linear Equations. Academic Press
    • (ed.), Oxford, Apr
    • Reid, J.K. (ed.): Large Sparse Sets of Linear Equations. Academic Press, New York (1971). (Oxford, Apr. 1970)
    • (1970) New York , vol.1971
    • Reid, J.K.1
  • 320
    • 84925466854 scopus 로고    scopus 로고
    • A massively parallel geometric multigrid solver on hierarchically distributed grids
    • Reiter, S., Vogel, A., Heppner, I., Rupp, M., Wittum, G.: A massively parallel geometric multigrid solver on hierarchically distributed grids. Comput. Vis. Sci. 16, 151–164 (2013)
    • (2013) Comput. Vis. Sci. , vol.16 , pp. 151-164
    • Reiter, S.1    Vogel, A.2    Heppner, I.3    Rupp, M.4    Wittum, G.5
  • 321
    • 0004550557 scopus 로고
    • Steplength optimization and linear multigrid methods
    • Reusken, A.: Steplength optimization and linear multigrid methods. Numer. Math. 58, 819–838 (1991)
    • (1991) Numer. Math. , vol.58 , pp. 819-838
    • Reusken, A.1
  • 322
    • 0026974530 scopus 로고
    • On maximum norm convergence of multigrid methods for two-point boundary value problems
    • Reusken, A.: On maximum norm convergence of multigrid methods for two-point boundary value problems. SIAM J. Numer. Anal. 29, 1569–1578 (1992)
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1569-1578
    • Reusken, A.1
  • 323
    • 0012960018 scopus 로고    scopus 로고
    • The smoothing property for regular splittings
    • ], pp
    • Reusken, A.: The smoothing property for regular splittings. In: Hackbusch and Wittum [208], pp. 130–138
    • Hackbusch and Wittum , vol.208 , pp. 130-138
    • Reusken, A.1
  • 324
    • 0000170864 scopus 로고
    • The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam
    • Richardson, L.F.: The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. Philosophical Transactions of the Royal Society of London, Series A 210, 307–357 (1910)
    • (1910) Philosophical Transactions of the Royal Society of London, Series A , vol.210 , pp. 307-357
    • Richardson, L.F.1
  • 327
    • 0012650693 scopus 로고
    • Ueber die numerische Auflösung von Differentialgleichungen
    • Runge, C.D.T.: Ueber die numerische Auflösung von Differentialgleichungen. Math. Ann. 46, 167–178 (1895)
    • (1895) Math. Ann. , vol.46 , pp. 167-178
    • Runge, C.D.T.1
  • 329
    • 0000048673 scopus 로고
    • : A generalized minimal residual method for solving nonsymmetric linear systems
    • Saad, Y., Schultz, M.H.: A generalized minimal residual method for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7, 856–869 (1986)
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 332
    • 84869495056 scopus 로고    scopus 로고
    • Krylov-type methods for tensor computations I
    • Savas, B., Eldén, L.: Krylov-type methods for tensor computations I. Linear Algebra Appl. 438, 891–918 (2013)
    • (2013) Linear Algebra Appl , vol.438 , pp. 891-918
    • Savas, B.1    Eldén, L.2
  • 333
    • 4244059578 scopus 로고
    • Reduktionsverfahren für Differenzengleichungen I
    • Schröder, J., Trottenberg, U.: Reduktionsverfahren für Differenzengleichungen I. Numer. Math. 22, 37–68 (1973)
    • (1973) Numer. Math. , vol.22 , pp. 37-68
    • Schröder, J.1    Trottenberg, U.2
  • 334
    • 85067963496 scopus 로고
    • Elliptic Problem Solvers. Academic Press, New York (1981)
    • (ed.), June
    • Schultz, M. H. (ed.): Elliptic Problem Solvers. Academic Press, New York (1981). (Santa Fe, June 1980)
    • (1980) (Santa Fe
    • Schultz, M.H.1
  • 335
    • 33746346426 scopus 로고    scopus 로고
    • Karhunen-Loève approximation of random fields by generalized fast multipole methods
    • Schwab, C., Todor, R.A.: Karhunen-Loève approximation of random fields by generalized fast multipole methods. J. Comput. Phys. 217, 100–122 (2006)
    • (2006) J. Comput. Phys. , vol.217 , pp. 100-122
    • Schwab, C.1    Todor, R.A.2
  • 336
    • 0001729306 scopus 로고
    • Über einen Grenzübergang durch alternierende Verfahren. Vierteljahres-schrift der
    • Schwarz, H. A.: Über einen Grenzübergang durch alternierende Verfahren. Vierteljahres-schrift der Naturforschenden Gesellschaft in Zürich 15, 272–286 (1870)
    • (1870) Naturforschenden Gesellschaft in Zürich , vol.15 , pp. 272-286
    • Schwarz, H.A.1
  • 337
    • 0005722921 scopus 로고
    • Über ein Verfahren, die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineare Gleichungen überhaupt, durch successive Annäherung aufzu-lösen
    • Seidel, P.L.: Über ein Verfahren, die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineare Gleichungen überhaupt, durch successive Annäherung aufzu-lösen. Abhandlungen der Mathematisch-Physikalischen Klasse der Königlich Bayerischen Akademie der Wissenschaften 11, 81–108 (1874)
    • (1874) Abhandlungen Der Mathematisch-Physikalischen Klasse Der Königlich Bayerischen Akademie Der Wissenschaften , vol.11 , pp. 81-108
    • Seidel, P.L.1
  • 339
    • 84968487134 scopus 로고
    • On the numerical solution of elliptic difference equations
    • Sheldon, J.: On the numerical solution of elliptic difference equations. Math. Tables and Other Aids to Computation 9, 101–112 (1955)
    • (1955) Math. Tables and Other Aids to Computation , vol.9 , pp. 101-112
    • Sheldon, J.1
  • 340
    • 85067994838 scopus 로고
    • Approximation Theory and Spline Functions. Reidel Publ
    • (eds.), Newfoundland, Aug./Sep
    • Singh, S.P., Burry, J.W.H., Watson, B. (eds.): Approximation Theory and Spline Functions. Reidel Publ., Dordrecht (1984). (Newfoundland, Aug./Sep. 1983)
    • (1983) Dordrecht , vol.1984
    • Singh, S.P.1    Burry, J.W.H.2    Watson, B.3
  • 341
    • 84966248432 scopus 로고
    • Iterative refinement implies numerical stability for Gaussian elimination
    • Skeel, R.D.: Iterative refinement implies numerical stability for Gaussian elimination. Math. Comp. 35, 817–832 (1980)
    • (1980) Math. Comp. , vol.35 , pp. 817-832
    • Skeel, R.D.1
  • 342
    • 0012031768 scopus 로고
    • Effect of equilibration on residual size of partial pivoting
    • Skeel, R.D.: Effect of equilibration on residual size of partial pivoting. SIAM J. Numer. Anal. 18, 449–454 (1981)
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 449-454
    • Skeel, R.D.1
  • 344
    • 0002716979 scopus 로고
    • CGS, a fast Lanczos-type solver for nonsymmetric linear systems
    • Sonneveld, P.: CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 10, 36–52 (1989)
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 36-52
    • Sonneveld, P.1
  • 345
    • 85067996173 scopus 로고    scopus 로고
    • Multigrid and conjugate gradient methods as convergence acceleration techniques
    • ], pp
    • Sonneveld, P., Wesseling, P., de Zeeuw, P.M.: Multigrid and conjugate gradient methods as convergence acceleration techniques. In: Paddon and Holstein [306], pp. 117–168
    • Paddon and Holstein , vol.306 , pp. 117-168
    • Sonneveld, P.1    Wesseling, P.2    de Zeeuw, P.M.3
  • 346
    • 0002466742 scopus 로고
    • Stress-calculation in frameworks by the method of “systematic relaxation of constraints”, parts I–II
    • Southwell, R.V.: Stress-calculation in frameworks by the method of “systematic relaxation of constraints”, parts I–II. Proc. Roy. Soc. Edinburgh Sect. A 151, 56–95 (1935)
    • (1935) Proc. Roy. Soc. Edinburgh Sect. A , vol.151 , pp. 56-95
    • Southwell, R.V.1
  • 347
    • 0009358004 scopus 로고
    • Stress-calculation in frameworks by the method of “systematic relaxation of constraints”, part III
    • Southwell, R.V.: Stress-calculation in frameworks by the method of “systematic relaxation of constraints”, part III. Proc. Roy. Soc. Edinburgh Sect. A 153, 41–76 (1935)
    • (1935) Proc. Roy. Soc. Edinburgh Sect. A , vol.153 , pp. 41-76
    • Southwell, R.V.1
  • 350
    • 0026239062 scopus 로고
    • Optimal ADI parameter for nonsymmetric systems of linear equations
    • Starke, G.: Optimal ADI parameter for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 28, 1431–1445 (1991)
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1431-1445
    • Starke, G.1
  • 352
    • 0005748664 scopus 로고
    • On the solution of linear simultaneous equations by iteration
    • Stein, P., Rosenberg, R. L.: On the solution of linear simultaneous equations by iteration. J. London Math. Soc. 23, 111–118 (1948)
    • (1948) J. London Math. Soc. , vol.23 , pp. 111-118
    • Stein, P.1    Rosenberg, R.L.2
  • 353
    • 0040391608 scopus 로고
    • Über einige Methoden der Relaxationsrechnung
    • Stiefel, E.: Über einige Methoden der Relaxationsrechnung. Z. Angew. Math. Phys. 3, 1–33 (1952)
    • (1952) Z. Angew. Math. Phys. , vol.3 , pp. 1-33
    • Stiefel, E.1
  • 354
    • 51249194447 scopus 로고
    • Relaxationsmethoden bester Strategie zur Lösung linearer Gleichungssysteme
    • Stiefel, E.: Relaxationsmethoden bester Strategie zur Lösung linearer Gleichungssysteme. Comment. Math. Helv. 29, 157–179 (1955)
    • (1955) Comment. Math. Helv. , vol.29 , pp. 157-179
    • Stiefel, E.1
  • 355
    • 85067951575 scopus 로고    scopus 로고
    • Stoer, J.: Solution of large systems of linear equations by conjugate gradient type methods. In: Bachem et al. [22], pp. 540–565
    • Stoer, J.1
  • 356
    • 0000564676 scopus 로고
    • Iterative solution of implicit approximations of multi-dimensional partial differential equations
    • Stone, H.L.: Iterative solution of implicit approximations of multi-dimensional partial differential equations. SIAM J. Numer. Anal. 5, 530–558 (1968)
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 530-558
    • Stone, H.L.1
  • 357
    • 0000685145 scopus 로고
    • On the real convergence rate of the conjugate gradient method
    • Strakos, Z.: On the real convergence rate of the conjugate gradient method. Linear Algebra Appl. 154, 535–549 (1991)
    • (1991) Linear Algebra Appl , vol.154 , pp. 535-549
    • Strakos, Z.1
  • 359
    • 0002621183 scopus 로고
    • Algebraic multigrid (AMG): Experiences and comparisons
    • Stüben, K.: Algebraic multigrid (AMG): experiences and comparisons. Appl. Math. Comput. 13, 419–451 (1983)
    • (1983) Appl. Math. Comput. , vol.13 , pp. 419-451
    • Stüben, K.1
  • 360
    • 0035282142 scopus 로고    scopus 로고
    • A review of algebraic multigrid
    • Stüben, K.: A review of algebraic multigrid. J. Comput. Appl. Math. 128, 281–309 (2001)
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 281-309
    • Stüben, K.1
  • 361
    • 1542269554 scopus 로고
    • Projection method for solving a singular system of linear equations and its applications
    • Tanabe, K.: Projection method for solving a singular system of linear equations and its applications. Numer. Math. 17, 203–214 (1971)
    • (1971) Numer. Math. , vol.17 , pp. 203-214
    • Tanabe, K.1
  • 364
    • 84870727055 scopus 로고
    • A lecagy from E. I. Zolotarv (1847–1878)
    • Todd, J.: A lecagy from E. I. Zolotarv (1847–1878). Math. Intelligencer 10, 50–53 (1988)
    • (1988) Math. Intelligencer , vol.10 , pp. 50-53
    • Todd, J.1
  • 368
    • 0002090018 scopus 로고
    • Condition numbers and equilibrium matrices
    • van der Sluis, A.: Condition numbers and equilibrium matrices. Numer. Math. 14, 14–23 (1969)
    • (1969) Numer. Math. , vol.14 , pp. 14-23
    • van der Sluis, A.1
  • 369
    • 34250492649 scopus 로고
    • Condition, equilibration and pivoting in linear algebraic systems
    • van der Sluis, A.: Condition, equilibration and pivoting in linear algebraic systems. Numer. Math. 15, 74–86 (1970)
    • (1970) Numer. Math. , vol.15 , pp. 74-86
    • van der Sluis, A.1
  • 370
    • 0001403122 scopus 로고
    • The rate of convergence of conjugate gradients
    • van der Sluis, A., van der Vorst, H.A.: The rate of convergence of conjugate gradients. Numer. Math. 48, 543–560 (1986)
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • van der Sluis, A.1    van der Vorst, H.A.2
  • 371
    • 0001259654 scopus 로고
    • A vectorizable variant of some ICCG methods
    • van der Vorst, H.A.: A vectorizable variant of some ICCG methods. SIAM J. Sci. Statist. Comput. 3, 350–356 (1982)
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 350-356
    • van der Vorst, H.A.1
  • 372
    • 0000005482 scopus 로고
    • A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • van der Vorst, H.A.: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 13, 631–644 (1992)
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • van der Vorst, H.A.1
  • 379
    • 0003435748 scopus 로고    scopus 로고
    • A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques
    • Verfürth, R.: A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques. J. Wiley and Teubner, Stuttgart (1996)
    • (1996) J. Wiley and Teubner, Stuttgart
    • Verfürth, R.1
  • 382
    • 0000871354 scopus 로고
    • Optimum alternating-direction-implicit iteration parameters for a model problem
    • Wachspress, E.L.: Optimum alternating-direction-implicit iteration parameters for a model problem. J. Soc. Indust. Appl. Math. 10, 339–350 (1962)
    • (1962) J. Soc. Indust. Appl. Math. , vol.10 , pp. 339-350
    • Wachspress, E.L.1
  • 384
    • 0000746513 scopus 로고
    • An alternating-direction-implicit iteration technique
    • Wachspress, E. L., Habetler, G. J.: An alternating-direction-implicit iteration technique. J. Soc. Indust. Appl. Math. 8, 403–424 (1960)
    • (1960) J. Soc. Indust. Appl. Math. , vol.8 , pp. 403-424
    • Wachspress, E.L.1    Habetler, G.J.2
  • 385
    • 0031313906 scopus 로고    scopus 로고
    • Tangential frequency filtering decompositions for symmetric matrices
    • Wagner, C.: Tangential frequency filtering decompositions for symmetric matrices. Numer. Math. 78, 119–142 (1997)
    • (1997) Numer. Math. , vol.78 , pp. 119-142
    • Wagner, C.1
  • 386
    • 0031328356 scopus 로고    scopus 로고
    • Tangential frequency filtering decompositions for unsymmetric matrices
    • Wagner, C.: Tangential frequency filtering decompositions for unsymmetric matrices. Numer. Math. 78, 143–163 (1997)
    • (1997) Numer. Math. , vol.78 , pp. 143-163
    • Wagner, C.1
  • 387
    • 0031327622 scopus 로고    scopus 로고
    • Adaptive filtering
    • Wagner, C., Wittum, G.: Adaptive filtering. Numer. Math. 78, 305–328 (1997)
    • (1997) Numer. Math. , vol.78 , pp. 305-328
    • Wagner, C.1    Wittum, G.2
  • 388
    • 0000043097 scopus 로고
    • Implementation of the GMRES method using Householder transformations
    • Walker, H.: Implementation of the GMRES method using Householder transformations. SIAM J. Sci. Statist. Comput. 9, 152–163 (1988)
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 152-163
    • Walker, H.1
  • 390
    • 0031366320 scopus 로고    scopus 로고
    • Parallel frequency filtering
    • Weiler, W., Wittum, G.: Parallel frequency filtering. Computing 58, 303–316 (1997)
    • (1997) Computing , vol.58 , pp. 303-316
    • Weiler, W.1    Wittum, G.2
  • 391
    • 84946384477 scopus 로고
    • Über das Iterationsverfahren
    • Weissinger, J.: Über das Iterationsverfahren. ZAMM 31, 245–246 (1951)
    • (1951) ZAMM , vol.31 , pp. 245-246
    • Weissinger, J.1
  • 393
    • 0001219259 scopus 로고    scopus 로고
    • A robust and efficient multigrid method
    • ], pp
    • Wesseling, P.: A robust and efficient multigrid method. In: Hackbusch and Trottenberg [205], pp. 614–630
    • Hackbusch and Trottenberg [205 , pp. 614-630
    • Wesseling, P.1
  • 394
    • 0001424303 scopus 로고
    • Theoretical and practical aspects of a multigrid method
    • Wesseling, P.: Theoretical and practical aspects of a multigrid method. SIAM J. Sci. Statist. Comput. 3, 387–407 (1982)
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 387-407
    • Wesseling, P.1
  • 395
    • 41149148546 scopus 로고
    • An Introduction to Multigrid Methods
    • Wesseling, P.: An Introduction to Multigrid Methods. Wiley, Chichester (1991)
    • (1991) Wiley, Chichester
    • Wesseling, P.1
  • 396
    • 0011053371 scopus 로고
    • A Lanczos method for a class of nonsymmetric systems of linear equations
    • Widlund, O.B.: A Lanczos method for a class of nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 15, 801–812 (1978)
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 801-812
    • Widlund, O.B.1
  • 397
    • 85067931453 scopus 로고    scopus 로고
    • Widlund, O.B.: Iterative substructuring methods: algorithms and theory for elliptic problems in the plane. In: Glowinski et al. [150], pp. 113–128
    • Widlund, O.B.1
  • 402
    • 0007370521 scopus 로고
    • Linear iterations as smoothers in multigrid methods: Theory with applications to incomplete decompositions
    • Wittum, G.: Linear iterations as smoothers in multigrid methods: theory with applications to incomplete decompositions. Impact Comput. Sci. Eng. 1, 180–215 (1989)
    • (1989) Impact Comput. Sci. Eng. , vol.1 , pp. 180-215
    • Wittum, G.1
  • 403
    • 0000561596 scopus 로고
    • On the robustness of ILU smoothing
    • Wittum, G.: On the robustness of ILU smoothing. SIAM J. Sci. Statist. Comput. 10, 699–717 (1989)
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 699-717
    • Wittum, G.1
  • 404
    • 85035133900 scopus 로고    scopus 로고
    • An ILU-based smoothing correction scheme
    • ], pp
    • Wittum, G.: An ILU-based smoothing correction scheme. In: Hackbusch [187], pp. 228–240
    • Hackbusch [187 , pp. 228-240
    • Wittum, G.1
  • 406
    • 0010608952 scopus 로고
    • On truncated incomplete decompositions
    • Wittum, G., Liebau, F.: On truncated incomplete decompositions. BIT 29, 719–740 (1989)
    • (1989) BIT , vol.29 , pp. 719-740
    • Wittum, G.1    Liebau, F.2
  • 408
    • 0026846317 scopus 로고
    • A new class of iterative methods for nonselfadjoint or indefinite problems
    • Xu, J.: A new class of iterative methods for nonselfadjoint or indefinite problems. SIAM J. Numer. Anal. 29, 303–319 (1992)
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 303-319
    • Xu, J.1
  • 409
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34, 581–613 (1992)
    • (1992) SIAM Rev , vol.34 , pp. 581-613
    • Xu, J.1
  • 410
    • 85020450077 scopus 로고    scopus 로고
    • Algebraic multigrid methods
    • To appear
    • Xu, J., Zikatonov, L.: Algebraic multigrid methods. Acta Numerica 26 (2017). To appear
    • (2017) Acta Numerica , vol.26
    • Xu, J.1    Zikatonov, L.2
  • 413
    • 0024666333 scopus 로고
    • A historical overview of iterative methods
    • Young, D.M.: A historical overview of iterative methods. Comput. Phys. Comm. 53, 1–17 (1989)
    • (1989) Comput. Phys. Comm. , vol.53 , pp. 1-17
    • Young, D.M.1
  • 415
    • 0021937208 scopus 로고
    • Hierarchical bases of finite element spaces in the discretization of non-symmetric elliptic boundary value problems
    • Yserentant, H.: Hierarchical bases of finite element spaces in the discretization of non-symmetric elliptic boundary value problems. Computing 35, 39–49 (1985)
    • (1985) Computing , vol.35 , pp. 39-49
    • Yserentant, H.1
  • 416
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • Yserentant, H.: On the multi-level splitting of finite element spaces. Numer. Math. 49, 379–412 (1986)
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Yserentant, H.1
  • 417
    • 0000760561 scopus 로고
    • Two preconditioners based on the multi-level splitting of finite element spaces
    • Yserentant, H.: Two preconditioners based on the multi-level splitting of finite element spaces. Numer. Math. 58, 163–184 (1990)
    • (1990) Numer. Math. , vol.58 , pp. 163-184
    • Yserentant, H.1


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