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Volumn 123, Issue 1-2, 2000, Pages 1-33

Iterative solution of linear systems in the 20th century

Author keywords

ADI; Krylov subspace methods; Multigrid; Polynomial acceleration; Preconditioning; Relaxation methods; SOR; Sparse approximate inverse

Indexed keywords

ALGORITHMS; INVERSE PROBLEMS; LINEAR ALGEBRA; LINEAR SYSTEMS; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING; RELAXATION PROCESSES;

EID: 0039179703     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00412-X     Document Type: Article
Times cited : (374)

References (208)
  • 1
    • 0001750069 scopus 로고
    • Solving sparse triangular systems on parallel computers
    • Anderson E.C., Saad Y. Solving sparse triangular systems on parallel computers. Internat. J. High Speed Comput. 1:1989;73-96.
    • (1989) Internat. J. High Speed Comput. , vol.1 , pp. 73-96
    • Anderson, E.C.1    Saad, Y.2
  • 2
    • 0002807741 scopus 로고
    • The principle of minimized iteration in the solution of the matrix eigenvalue problem
    • Arnoldi W.E. The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Appl. Math. 9:1951;17-29.
    • (1951) Quart. Appl. Math. , vol.9 , pp. 17-29
    • Arnoldi, W.E.1
  • 3
    • 0001160426 scopus 로고
    • A generalized SSOR method
    • Axelsson O. A generalized SSOR method. BIT. 12:1972;443-467.
    • (1972) BIT , vol.12 , pp. 443-467
    • Axelsson, O.1
  • 4
    • 0041066350 scopus 로고
    • Solution of linear systems of equations: iterative methods
    • in: V.A. Barker (Ed.), Springer, Berlin, Copenhagen
    • O. Axelsson, Solution of linear systems of equations: iterative methods, in: V.A. Barker (Ed.), Sparse Matrix Techniques, Springer, Berlin, 1977, Copenhagen, 1976, pp. 1-51.
    • (1976) Sparse Matrix Techniques , pp. 1-51
    • Axelsson, O.1
  • 5
    • 0002205748 scopus 로고
    • Conjugate gradient type-methods for unsymmetric and inconsistent systems of linear equations
    • Axelsson O. Conjugate gradient type-methods for unsymmetric and inconsistent systems of linear equations. Linear Algebra Appl. 29:1980;1-16.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 1-16
    • Axelsson, O.1
  • 6
    • 38249042495 scopus 로고
    • A general incomplete block-factorization method
    • Axelsson O. A general incomplete block-factorization method. Linear Algebra Appl. 74:1986;179-190.
    • (1986) Linear Algebra Appl. , vol.74 , pp. 179-190
    • Axelsson, O.1
  • 8
    • 0001276831 scopus 로고
    • On the eigenvalue distribution of a class of preconditioning methods
    • Axelsson O., Lindskog G. On the eigenvalue distribution of a class of preconditioning methods. Numer. Math. 48:1986;479-498.
    • (1986) Numer. Math. , vol.48 , pp. 479-498
    • Axelsson, O.1    Lindskog, G.2
  • 9
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods, I
    • Axelsson O., Vassilevski P. Algebraic multilevel preconditioning methods, I. Numer. Math. 56:1989;157-177.
    • (1989) Numer. Math. , vol.56 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.2
  • 10
    • 0001573921 scopus 로고
    • Algebraic multilevel preconditioning methods, II
    • Axelsson O., Vassilevski P. Algebraic multilevel preconditioning methods, II. SIAM J. Numer. Anal. 27(6):1990;1569-1590.
    • (1990) SIAM J. Numer. Anal. , vol.27 , Issue.6 , pp. 1569-1590
    • Axelsson, O.1    Vassilevski, P.2
  • 11
    • 0001116752 scopus 로고
    • A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning
    • Axelsson O., Vassilevski P.S. A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning. SIAM J. Matrix Anal. Appl. 12(4):1991;625-644.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , Issue.4 , pp. 625-644
    • Axelsson, O.1    Vassilevski, P.S.2
  • 12
    • 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. 66:1993;295-319.
    • (1993) Numer. Math. , vol.66 , pp. 295-319
    • Bank, R.E.1    Chan, T.F.2
  • 16
    • 0000131670 scopus 로고
    • Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems
    • Benson M.W., Frederickson P.O. Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems. Utilitas Math. 22:1982;127-140.
    • (1982) Utilitas Math. , vol.22 , pp. 127-140
    • Benson, M.W.1    Frederickson, P.O.2
  • 17
    • 0000133360 scopus 로고    scopus 로고
    • A two-level parallel preconditioner based on sparse approximate inverses
    • in: D.R. Kincaid, A.C. Elster (Eds.), II, IMACS, New Brunswick, NJ
    • M. Benzi, J. Marín, M. Tůma, A two-level parallel preconditioner based on sparse approximate inverses, in: D.R. Kincaid, A.C. Elster (Eds.), Iterative Methods in Scientific Computation, II, IMACS, New Brunswick, NJ, 1999, pp. 167-178.
    • (1999) Iterative Methods in Scientific Computation , pp. 167-178
    • Benzi, M.1    Marín, J.2    Tůma, M.3
  • 18
    • 0004675411 scopus 로고    scopus 로고
    • A sparse approximate inverse preconditioner for the conjugate gradient method
    • Benzi M., Meyer C.D., Tůma M. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput. 17:1996;1135-1149.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 1135-1149
    • Benzi, M.1    Meyer, C.D.2    Tůma, M.3
  • 19
    • 0033293791 scopus 로고    scopus 로고
    • Orderings for incomplete factorization preconditioning of nonsymmetric problems
    • Benzi M., Szyld D.B., van Duin A. Orderings for incomplete factorization preconditioning of nonsymmetric problems. SIAM J. Sci. Comput. 20:1999;1652-1670.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1652-1670
    • Benzi, M.1    Szyld, D.B.2    Van Duin, A.3
  • 20
  • 21
    • 0040472190 scopus 로고
    • Solving elliptic problems: 1930-1980
    • M.H. Schultz. New York: Academic Press
    • Birkhoff G. Solving elliptic problems: 1930-1980. Schultz M.H. Elliptic Problem Solver. 1981;17-38 Academic Press, New York.
    • (1981) Elliptic Problem Solver , pp. 17-38
    • Birkhoff, G.1
  • 22
    • 0018711879 scopus 로고
    • Accelerated projection methods for computing pseudo-inverse solutions of systems of linear equations
    • Björck A., Elfving T. Accelerated projection methods for computing pseudo-inverse solutions of systems of linear equations. BIT. 19:1979;145-163.
    • (1979) BIT , vol.19 , pp. 145-163
    • Björck, A.1    Elfving, T.2
  • 25
    • 0000713765 scopus 로고
    • Row projection methods for large nonsymmetric linear systems
    • Bramley R., Sameh A. Row projection methods for large nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 13:1992;168-193.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 168-193
    • Bramley, R.1    Sameh, A.2
  • 26
    • 0012223973 scopus 로고
    • Multi-level adaptive technique (MLAT) for fast numerical solutions to boundary problems
    • in: H. Cabannes, R. Temam (Eds.), Paris, Springer, Berlin
    • A. Brandt, Multi-level adaptive technique (MLAT) for fast numerical solutions to boundary problems, in: H. Cabannes, R. Temam (Eds.), Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Paris, 1972, Springer, Berlin, 1973, pp. 82-89.
    • (1972) Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics , pp. 82-89
    • Brandt, A.1
  • 27
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary value problems
    • Brandt A. Multi-level adaptive solutions to boundary value problems. Math. Comp. 31:1977;333-390.
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 30
    • 34249762279 scopus 로고
    • Look-ahead in bicgstab and other product methods for linear systems
    • Brezinski C., Redivo-Zaglia M. Look-ahead in bicgstab and other product methods for linear systems. BIT. 35:1995;169-201.
    • (1995) BIT , vol.35 , pp. 169-201
    • Brezinski, C.1    Redivo-Zaglia, M.2
  • 31
    • 0001595068 scopus 로고
    • Avoiding breakdown and near-breakdown in Lanczos type algorithms
    • Brezinski C., Redivo-Zaglia M., Sadok H. Avoiding breakdown and near-breakdown in Lanczos type algorithms. Numer. Algorithms. 1:1991;261-284.
    • (1991) Numer. Algorithms , vol.1 , pp. 261-284
    • Brezinski, C.1    Redivo-Zaglia, M.2    Sadok, H.3
  • 32
    • 21144473062 scopus 로고
    • A breakdown-free Lanczos' type algorithm for solving linear systems
    • Brezinski C., Redivo-Zaglia M., Sadok H. A breakdown-free Lanczos' type algorithm for solving linear systems. Numer. Math. 63:1992;29-38.
    • (1992) Numer. Math. , vol.63 , pp. 29-38
    • Brezinski, C.1    Redivo-Zaglia, M.2    Sadok, H.3
  • 34
    • 0002864202 scopus 로고
    • A theoretical comparison of the Arnoldi and GMRES algorithms
    • Brown P.N. A theoretical comparison of the Arnoldi and GMRES algorithms. SIAM J. Sci. Statist. Comput. 12:1991;58-78.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 58-78
    • Brown, P.N.1
  • 35
    • 77957174880 scopus 로고
    • A new method of solving nonlinear simultaneous equations
    • Broyden G.C. A new method of solving nonlinear simultaneous equations. Comput. J. 12:1969;94-99.
    • (1969) Comput. J. , vol.12 , pp. 94-99
    • Broyden, G.C.1
  • 36
    • 0001045889 scopus 로고
    • A numerical method for the solution of two-dimensional and three-dimensional equations of diffusion
    • (in Russian)
    • N.I. Buleev, A numerical method for the solution of two-dimensional and three-dimensional equations of diffusion, Math. Sb. 51 (1960) 227-238 (in Russian).
    • (1960) Math. Sb. , vol.51 , pp. 227-238
    • Buleev, N.I.1
  • 37
    • 0001348998 scopus 로고
    • Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive
    • Cesari L. Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive. Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. Ser. 6a. 25:1937;422-428.
    • (1937) Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. Ser. 6a , vol.25 , pp. 422-428
    • Cesari, L.1
  • 38
    • 0001394997 scopus 로고
    • A quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric systems
    • Chan T.F., Gallopoulos E., Simoncini V., Szeto T., Tong C.H. A quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric systems. SIAM J. Sci. Comput. 15:1994;338-347.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 338-347
    • Chan, T.F.1    Gallopoulos, E.2    Simoncini, V.3    Szeto, T.4    Tong, C.H.5
  • 39
    • 0013240081 scopus 로고
    • A note on the efficiency of domain decomposed incomplete factorizations
    • Chan T.F., Goovaerts D. A note on the efficiency of domain decomposed incomplete factorizations. SIAM J. Sci. Statist. Comput. 11:1990;794-803.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 794-803
    • Chan, T.F.1    Goovaerts, D.2
  • 42
    • 0031261348 scopus 로고    scopus 로고
    • Approximate inverse techniques for block-partitioned matrices
    • Chow E., Saad Y. Approximate inverse techniques for block-partitioned matrices. SIAM J. Sci. Comput. 18:1997;1657-1675.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1657-1675
    • Chow, E.1    Saad, Y.2
  • 43
    • 0001630026 scopus 로고    scopus 로고
    • Approximate inverse preconditioners via sparse-sparse iterations
    • Chow E., Saad Y. Approximate inverse preconditioners via sparse-sparse iterations. SIAM J. Sci. Comput. 19:1998;995-1023.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 995-1023
    • Chow, E.1    Saad, Y.2
  • 44
    • 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. Ric. Sci. Progr. Tecn. Econom. Naz. 9:1938;326-333.
    • (1938) Ric. Sci. Progr. Tecn. Econom. Naz. , vol.9 , pp. 326-333
    • Cimmino, G.1
  • 45
    • 0002576532 scopus 로고
    • A generalized conjugate gradient method for nonsymmetric systems of linear equations
    • R. Glowinski, & J.L. Lions. New York: Springer
    • Concus P., Golub G.H. A generalized conjugate gradient method for nonsymmetric systems of linear equations. Glowinski R., Lions J.L. Computing Methods in Applied Sciences and Engineering. 1976;56-65 Springer, New York.
    • (1976) Computing Methods in Applied Sciences and Engineering , pp. 56-65
    • Concus, P.1    Golub, G.H.2
  • 47
    • 0002540389 scopus 로고
    • A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations
    • J.R. Bunch, & D.J. Rose. New York: Academic Press
    • Concus P., Golub G.H., O'Leary D.P. A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations. Bunch J.R., Rose D.J. Sparse Matrix Computations. 1976;309-332 Academic Press, New York.
    • (1976) Sparse Matrix Computations , pp. 309-332
    • Concus, P.1    Golub, G.H.2    O'Leary, D.P.3
  • 49
    • 0030542825 scopus 로고    scopus 로고
    • Relations between Galerkin and norm-minimizing iterative methods for solving linear systems
    • Cullum J., Greenbaum A. Relations between Galerkin and norm-minimizing iterative methods for solving linear systems. SIAM J. Matrix Anal. Appl. 17:1996;223-247.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 223-247
    • Cullum, J.1    Greenbaum, A.2
  • 50
    • 0001810214 scopus 로고
    • The conjugate gradient method for linear and nonlinear operator equations
    • Daniel J.W. The conjugate gradient method for linear and nonlinear operator equations. SIAM J. Numer. Anal. 4:1967;10-26.
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 10-26
    • Daniel, J.W.1
  • 52
    • 0000565358 scopus 로고
    • Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
    • D'Azevedo E.F., Forsyth F.A., Tang W.P. Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems. SIAM J. Matrix Anal. Appl. 13:1992;944-961.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 944-961
    • D'Azevedo, E.F.1    Forsyth, F.A.2    Tang, W.P.3
  • 53
    • 0000256195 scopus 로고
    • Towards a cost effective ILU preconditioner with high level fill
    • D'Azevedo E.F., Forsyth F.A., Tang W.P. Towards a cost effective ILU preconditioner with high level fill. BIT. 31:1992;442-463.
    • (1992) BIT , vol.31 , pp. 442-463
    • D'Azevedo, E.F.1    Forsyth, F.A.2    Tang, W.P.3
  • 54
    • 0039991521 scopus 로고
    • Extremal polynomials with applications to Richardson iteration for indefinite systems
    • de Boor C., Rice J.R. Extremal polynomials with applications to Richardson iteration for indefinite systems. SIAM J. Sci. Statist. Comput. 3:1982;47-57.
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 47-57
    • De Boor, C.1    Rice, J.R.2
  • 55
    • 84932073219 scopus 로고
    • Gauss in seiner Vorlesung über die Methode der kleisten Quadrate
    • Dedekind R. Gauss in seiner Vorlesung über die Methode der kleisten Quadrate. Gesammelte Math. Werke. 2:1901;293-306.
    • (1901) Gesammelte Math. Werke , vol.2 , pp. 293-306
    • Dedekind, R.1
  • 58
    • 0018707156 scopus 로고
    • Approximating the inverse of a matrix for use on iterative algorithms on vectors processors
    • Dubois P.F., Greenbaum A., Rodrigue G.H. Approximating the inverse of a matrix for use on iterative algorithms on vectors processors. Computing. 22:1979;257-268.
    • (1979) Computing , vol.22 , pp. 257-268
    • Dubois, P.F.1    Greenbaum, A.2    Rodrigue, G.H.3
  • 59
    • 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. 29:1989;635-657.
    • (1989) BIT , vol.29 , pp. 635-657
    • Duff, I.S.1    Meurant, G.A.2
  • 60
    • 0000762041 scopus 로고
    • An approximate factorization procedure for solving self-adjoint elliptic difference equations
    • Dupont T., Kendall R., Rachford H. An approximate factorization procedure for solving self-adjoint elliptic difference equations. SIAM J. Numer. Anal. 5:1968;559-573.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 559-573
    • Dupont, T.1    Kendall, R.2    Rachford, H.3
  • 61
  • 62
    • 0000011239 scopus 로고
    • Variational iterative methods for nonsymmetric systems of linear equations
    • Eisenstat S.C., Elman H.C., Schultz M.H. Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20:1983;345-357.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 345-357
    • Eisenstat, S.C.1    Elman, H.C.2    Schultz, M.H.3
  • 63
    • 84966211825 scopus 로고
    • A stability analysis of incomplete LU factorizations
    • Elman H.C. A stability analysis of incomplete LU factorizations. Math. Comp. 47:1986;191-217.
    • (1986) Math. Comp. , vol.47 , pp. 191-217
    • Elman, H.C.1
  • 64
    • 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. 29:1989;890-915.
    • (1989) BIT , vol.29 , pp. 890-915
    • Elman, H.C.1
  • 65
    • 0000495623 scopus 로고
    • Line iterative methods for cyclically reduced discrete convection-diffusion problems
    • Elman H.C., Golub G.H. Line iterative methods for cyclically reduced discrete convection-diffusion problems. SIAM J. Sci. Statist. Comput. 13:1992;339-363.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 339-363
    • Elman, H.C.1    Golub, G.H.2
  • 66
    • 0001765691 scopus 로고
    • A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations
    • Elman H.C., Saad Y., Saylor P. A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations. SIAM J. Sci. Statist. Comput. 7:1986;840-855.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 840-855
    • Elman, H.C.1    Saad, Y.2    Saylor, P.3
  • 70
    • 0000234821 scopus 로고
    • The use of pre-conditioning in iterative methods for solving linear equations with symmetric positive definite matrices
    • Evans D.J. The use of pre-conditioning in iterative methods for solving linear equations with symmetric positive definite matrices. J. Inst. Math. Appl. 4:1968;295-314.
    • (1968) J. Inst. Math. Appl. , vol.4 , pp. 295-314
    • Evans, D.J.1
  • 71
    • 0021416130 scopus 로고
    • Necessary and sufficient conditions for the existence of a conjugate gradient method
    • Faber V., Manteuffel T. Necessary and sufficient conditions for the existence of a conjugate gradient method. SIAM J. Numer. Anal. 21:1984;352-361.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 352-361
    • Faber, V.1    Manteuffel, T.2
  • 73
    • 0001038302 scopus 로고
    • On the speed of convergence of an iteration process
    • Fedorenko R.P. On the speed of convergence of an iteration process. USSR Comput. Math. Math. Phys. 4:1964;227-235.
    • (1964) USSR Comput. Math. Math. Phys. , vol.4 , pp. 227-235
    • Fedorenko, R.P.1
  • 74
    • 0039879223 scopus 로고
    • A stable Richardson iteration method for complex linear systems
    • Fischer B., Reichel L. A stable Richardson iteration method for complex linear systems. Numer. Math. 54:1988;225-241.
    • (1988) Numer. Math. , vol.54 , pp. 225-241
    • Fischer, B.1    Reichel, L.2
  • 75
    • 0000617787 scopus 로고
    • Numerical determination of fundamental modes
    • Flanders D.A., Shortley G. Numerical determination of fundamental modes. J. Appl. Phys. 21:1950;1322-1328.
    • (1950) J. Appl. Phys. , vol.21 , pp. 1322-1328
    • Flanders, D.A.1    Shortley, G.2
  • 78
    • 84968466265 scopus 로고
    • Convergence rates of iterative treatments of partial differential equations
    • Frankel S. Convergence rates of iterative treatments of partial differential equations. MTAC. 1950;65-75.
    • (1950) MTAC , pp. 65-75
    • Frankel, S.1
  • 79
    • 0001031880 scopus 로고
    • A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
    • Freund R.W. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput. 14(2):1993;470-482.
    • (1993) SIAM J. Sci. Comput. , vol.14 , Issue.2 , pp. 470-482
    • Freund, R.W.1
  • 81
    • 25444452938 scopus 로고
    • QMR: A quasi-minimal residual method for non-Hermitian linear systems
    • Freund R.W., Nachtigal N.M. QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numer. Math. 60:1991;315-339.
    • (1991) Numer. Math. , vol.60 , pp. 315-339
    • Freund, R.W.1    Nachtigal, N.M.2
  • 82
    • 0000257658 scopus 로고
    • A parallel hybrid sparse linear system solver
    • Gallivan K., Sameh A., Zlatev Z. A parallel hybrid sparse linear system solver. Comput. Systems Eng. 1(2-4):1990;183-195.
    • (1990) Comput. Systems Eng. , vol.1 , Issue.24 , pp. 183-195
    • Gallivan, K.1    Sameh, A.2    Zlatev, Z.3
  • 85
    • 0039879232 scopus 로고
    • Application of the best approximation polynomial to improving the convergence of iterative methods
    • (in Russian)
    • M.K. Gavurin, Application of the best approximation polynomial to improving the convergence of iterative methods, Uspehi Mat. Nauk. 5(3) (1950) 156-160 (in Russian).
    • (1950) Uspehi Mat. Nauk. , vol.5 , Issue.3 , pp. 156-160
    • Gavurin, M.K.1
  • 86
    • 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. 31:1989;50-102.
    • (1989) SIAM Rev. , vol.31 , pp. 50-102
    • Golub, G.H.1    O'Leary, D.P.2
  • 87
    • 34250972588 scopus 로고
    • Chebyshev semi iterative methods successive overrelaxation iterative methods and second order Richardson iterative methods
    • Golub G.H., Varga R.S. Chebyshev semi iterative methods successive overrelaxation iterative methods and second order Richardson iterative methods. Numer. Math. 3:1961;147-168.
    • (1961) Numer. Math. , vol.3 , pp. 147-168
    • Golub, G.H.1    Varga, R.S.2
  • 89
    • 0000002780 scopus 로고
    • Predicting the behavior of finite precision Lanczos and conjugate gradient computations
    • Greenbaum A., Strakos Z. Predicting the behavior of finite precision Lanczos and conjugate gradient computations. SIAM J. Matrix Anal. Appl. 13:1992;121-137.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 121-137
    • Greenbaum, A.1    Strakos, Z.2
  • 90
    • 0002251447 scopus 로고
    • Matrices that generate the same Krylov residual spaces
    • G. Golub, M. Luskin, & A. Greenbaum. Recent Advances in Iterative Methods. New York: Springer
    • Greenbaum A., Strakos Z. Matrices that generate the same Krylov residual spaces. Golub G., Luskin M., Greenbaum A. Recent Advances in Iterative Methods. IMA Volumes in Mathematics and Its Applications. Vol. 60:1994;95-119 Springer, New York.
    • (1994) IMA Volumes in Mathematics and Its Applications , vol.60 , pp. 95-119
    • Greenbaum, A.1    Strakos, Z.2
  • 91
    • 0041049302 scopus 로고    scopus 로고
    • Any nonincreasing convergence curve is possible for GMRES
    • Greenbaum A., Ptak V., Strakoš Z. Any nonincreasing convergence curve is possible for GMRES. SIAM J. Matrix Anal. Appl. 17:1996;465-469.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 465-469
    • Greenbaum, A.1    Ptak, V.2    Strakoš, Z.3
  • 92
    • 0031129197 scopus 로고    scopus 로고
    • Parallel preconditioning with sparse approximate inverses
    • Grote M., Huckle T. Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18:1997;838-853.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 838-853
    • Grote, M.1    Huckle, T.2
  • 93
    • 0000919240 scopus 로고
    • Parallel preconditioning and approximate inverses on the connection machine
    • R.F. Sincovec, D.E. Keyes, L.R. Petzold, & D.A. Reed. Philadelphia, PA: SIAM
    • Grote M., Simon H.D. Parallel preconditioning and approximate inverses on the connection machine. Sincovec R.F., Keyes D.E., Petzold L.R., Reed D.A. Parallel Processing for Scientific Computing, Vol. 2. 1992;519-523 SIAM, Philadelphia, PA.
    • (1992) Parallel Processing for Scientific Computing, Vol. 2 , pp. 519-523
    • Grote, M.1    Simon, H.D.2
  • 94
    • 0003039594 scopus 로고
    • A class of first order factorization methods
    • Gustafsson I. A class of first order factorization methods. BIT. 18:1978;142-156.
    • (1978) BIT , vol.18 , pp. 142-156
    • Gustafsson, I.1
  • 95
    • 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. 13:1992;594-639.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 594-639
    • Gutknecht, M.H.1
  • 99
    • 0010007548 scopus 로고
    • Iterative methods of solving linear systems on Hilbert space
    • Hayes R.M. Iterative methods of solving linear systems on Hilbert space. National Bureau of Standards, Appl. Math. Ser. 39:1954;71-103.
    • (1954) National Bureau of Standards, Appl. Math. Ser. , vol.39 , pp. 71-103
    • Hayes, R.M.1
  • 100
    • 0012730774 scopus 로고
    • The conjugate-gradient method for solving linear systems
    • McGraw-Hill, New York
    • M.R. Hestenes, The conjugate-gradient method for solving linear systems, in: Sympos. Appl. Math., Numerical Analysis, Vol. VI, McGraw-Hill, New York, 1956, pp. 83-102.
    • (1956) In: Sympos. Appl. Math., Numerical Analysis , vol.6 , pp. 83-102
    • Hestenes, M.R.1
  • 103
    • 0001010277 scopus 로고
    • Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
    • Jea K.C., Young D.M. Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods. Linear Algebra Appl. 34:1980;159-194.
    • (1980) Linear Algebra Appl. , vol.34 , pp. 159-194
    • Jea, K.C.1    Young, D.M.2
  • 104
    • 0000051186 scopus 로고
    • Polynomial preconditionings for conjugate gradient calculations
    • Johnson O.G., Micchelli C.A., Paul G. Polynomial preconditionings for conjugate gradient calculations. SIAM J. Numer. Anal. 20:1983;362-376.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 362-376
    • Johnson, O.G.1    Micchelli, C.A.2    Paul, G.3
  • 106
    • 0001554939 scopus 로고
    • Angenäherte Auflösung von Systemen linearer Gleichungen
    • Kaczmarz S. Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Internat. Acad. Pol. Sci. Lett. A. 35:1937;355-357.
    • (1937) Bull. Internat. Acad. Pol. Sci. Lett. a , vol.35 , pp. 355-357
    • Kaczmarz, S.1
  • 108
    • 0024606847 scopus 로고
    • A projection method for solving nonsymmetric linear systems on multiprocessors
    • Kamath C., Sameh A. A projection method for solving nonsymmetric linear systems on multiprocessors. Parallel Comput. 9:1988; / 89 291-312.
    • (1988) Parallel Comput. , vol.9 , pp. 291-312
    • Kamath, C.1    Sameh, A.2
  • 109
    • 84968508687 scopus 로고
    • Estimates for some computational techniques in linear algebra
    • Kaniel S. Estimates for some computational techniques in linear algebra. Math. Comp. 20:1966;369-378.
    • (1966) Math. Comp. , vol.20 , pp. 369-378
    • Kaniel, S.1
  • 110
    • 0040472192 scopus 로고
    • On an efficient method for solving optimization problems for quadratic functionals
    • (in Russian)
    • L. Kantorovitch, On an efficient method for solving optimization problems for quadratic functionals, DAN SSSR 48(7) (1945) 7-8 (in Russian).
    • (1945) DAN SSSR , vol.48 , Issue.7 , pp. 7-8
    • Kantorovitch, L.1
  • 111
    • 84968510956 scopus 로고
    • Convergence of a method of solving linear problems
    • Karush W. Convergence of a method of solving linear problems. Proc. Amer. Math. Soc. 3:1952;839-851.
    • (1952) Proc. Amer. Math. Soc. , vol.3 , pp. 839-851
    • Karush, W.1
  • 112
    • 0000650635 scopus 로고
    • An iterative least-square method suitable for solving large sparse matrices
    • Khabaza I.M. An iterative least-square method suitable for solving large sparse matrices. Comput. J. 6:1963;202-206.
    • (1963) Comput. J. , vol.6 , pp. 202-206
    • Khabaza, I.M.1
  • 113
    • 0000747319 scopus 로고
    • On a family of two-level preconditionings of the incomplete block factorization type
    • Kolotilina L.Yu., Yeremin A.Yu. On a family of two-level preconditionings of the incomplete block factorization type. Soviet J. Numer. Anal. Math. Modelling. 1:1986;293-320.
    • (1986) Soviet J. Numer. Anal. Math. Modelling , vol.1 , pp. 293-320
    • Kolotilina, L.Yu.1    Yeremin, A.Yu.2
  • 114
    • 21144474663 scopus 로고
    • Factorized sparse approximate inverse preconditionings I, Theory
    • Kolotilina L.Yu., Yeremin A.Yu. Factorized sparse approximate inverse preconditionings I, Theory. SIAM J. Matrix Anal. Appl. 14:1993;45-58.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 45-58
    • Kolotilina, L.Yu.1    Yeremin, A.Yu.2
  • 115
    • 0000094594 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • Lanczos C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Standards. 45:1950;255-282.
    • (1950) J. Res. Nat. Bur. Standards , vol.45 , pp. 255-282
    • Lanczos, C.1
  • 116
    • 84897999325 scopus 로고
    • Chebyshev polynomials in the solution of large-scale linear systems
    • Lanczos C. Chebyshev polynomials in the solution of large-scale linear systems. Toronto Symposium on Computing Techniques. 1952;124-133.
    • (1952) Toronto Symposium on Computing Techniques , pp. 124-133
    • Lanczos, C.1
  • 117
    • 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. 49:1952;33-53.
    • (1952) J. Res. Nat. Bur. Standards , vol.49 , pp. 33-53
    • Lanczos, C.1
  • 118
    • 84914329370 scopus 로고
    • Die angenäherte harmonischer Funktionen und konformer Abbildungen (nach Ideen von Boltzmann und Jacobi)
    • Liebmann H. Die angenäherte harmonischer Funktionen und konformer Abbildungen (nach Ideen von Boltzmann und Jacobi). S. B. Math. Nat. Kl. Bayerischen Akad. Wiss. München. 1918;385-416.
    • (1918) S. B. Math. Nat. Kl. Bayerischen Akad. Wiss. München , pp. 385-416
    • Liebmann, H.1
  • 119
    • 0008368136 scopus 로고
    • Hyperbolic pairs in the method of conjugate gradients
    • Luenberger D.G. Hyperbolic pairs in the method of conjugate gradients. SIAM J. Appl. Math. 17:1979;1263-1267.
    • (1979) SIAM J. Appl. Math. , vol.17 , pp. 1263-1267
    • Luenberger, D.G.1
  • 120
    • 0008525751 scopus 로고
    • Modified block-approximate factorization strategies
    • Magolu M.M. Modified block-approximate factorization strategies. Numer. Math. 61:1992;91-110.
    • (1992) Numer. Math. , vol.61 , pp. 91-110
    • Magolu, M.M.1
  • 121
    • 0001585226 scopus 로고
    • Ordering strategies for modified block incomplete factorizations
    • Magolu M.M. Ordering strategies for modified block incomplete factorizations. SIAM J. Sci. Comput. 16:1995;378-399.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 378-399
    • Magolu, M.M.1
  • 122
    • 0001256129 scopus 로고
    • The Tchebychev iteration for nonsymmetric linear systems
    • Manteuffel T.A. The Tchebychev iteration for nonsymmetric linear systems. Numer. Math. 28:1977;307-327.
    • (1977) Numer. Math. , vol.28 , pp. 307-327
    • Manteuffel, T.A.1
  • 123
    • 0001063814 scopus 로고
    • Adaptive procedure for estimation of parameter for the nonsymmetric Tchebychev iteration
    • Manteuffel T.A. Adaptive procedure for estimation of parameter for the nonsymmetric Tchebychev iteration. Numer. Math. 28:1978;187-208.
    • (1978) Numer. Math. , vol.28 , pp. 187-208
    • Manteuffel, T.A.1
  • 125
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • Meijerink J.A., 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(137):1977;148-162.
    • (1977) Math. Comp. , vol.31 , Issue.137 , pp. 148-162
    • Meijerink, J.A.1    Van Der Vorst, H.A.2
  • 126
    • 49049148707 scopus 로고
    • Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems
    • Meijerink J.A., van der Vorst H.A. Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems. J. Comput. Phys. 44:1981;134-155.
    • (1981) J. Comput. Phys. , vol.44 , pp. 134-155
    • Meijerink, J.A.1    Van Der Vorst, H.A.2
  • 128
    • 0016487989 scopus 로고
    • Algorithmes de relaxation chaotiques á retard
    • Miellou J.C. Algorithmes de relaxation chaotiques á retard. RAIRO. R-1:1975;55-82.
    • (1975) RAIRO , vol.1 , pp. 55-82
    • Miellou, J.C.1
  • 130
    • 0040472193 scopus 로고
    • Determining unknowns using the least squares method when the number of unknowns is large
    • (in Russian)
    • P.A. Nekrasov, Determining unknowns using the least squares method when the number of unknowns is large, Mat. Sb. 12 (1884) 189-204 (in Russian).
    • (1884) Mat. Sb. , vol.12 , pp. 189-204
    • Nekrasov, P.A.1
  • 131
    • 84985417816 scopus 로고
    • DRIC: A dynamic version of the RIC method
    • Notay Y. DRIC: a dynamic version of the RIC method. Numer. Linear Algebra Appl. 1:1994;511-532.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 511-532
    • Notay, Y.1
  • 132
    • 0001399580 scopus 로고
    • An extrapolation process for solving linear systems
    • Oliphant T.A. An extrapolation process for solving linear systems. Quart. Appl. Math. 20:1962;257-267.
    • (1962) Quart. Appl. Math. , vol.20 , pp. 257-267
    • Oliphant, T.A.1
  • 133
    • 0001927801 scopus 로고
    • An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems
    • Oosterlee C.W., Washio T. An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems. SIAM J. Sci. Statist. Comput. 19:1991;87-110.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.19 , pp. 87-110
    • Oosterlee, C.W.1    Washio, T.2
  • 135
    • 13544261154 scopus 로고
    • Uber die Determinanten mit überwiegender Hauptdiagonale
    • Ostrowski A.M. Uber die Determinanten mit überwiegender Hauptdiagonale. Comment. Math. Helv. 10:1937;69-96.
    • (1937) Comment. Math. Helv. , vol.10 , pp. 69-96
    • Ostrowski, A.M.1
  • 136
    • 0005653333 scopus 로고
    • On the linear iteration procedures for symmetirc matrices
    • Ostrowski A.M. On the linear iteration procedures for symmetirc matrices. Rend. Mat. Appl. 14:1954;140-163.
    • (1954) Rend. Mat. Appl. , vol.14 , pp. 140-163
    • Ostrowski, A.M.1
  • 137
    • 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. 12:1975;617-629.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 138
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • Paige C.C., Saunders M.A. LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software. 8:1982;43-71.
    • (1982) ACM Trans. Math. Software , vol.8 , pp. 43-71
    • Paige, C.C.1    Saunders, M.A.2
  • 139
    • 0000131773 scopus 로고
    • Reduction to tridiagonal form and minimal realizations
    • Parlett B.N. Reduction to tridiagonal form and minimal realizations. SIAM J. Matrix Anal. Appl. 13:1992;567-593.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 567-593
    • Parlett, B.N.1
  • 140
    • 84966231631 scopus 로고
    • A look-ahead Lanczos algorithm for nonsymmetric matrices
    • Parlett B.N., Taylor D.R., Liu Z.S. A look-ahead Lanczos algorithm for nonsymmetric matrices. Math. Comp. 44:1985;105-124.
    • (1985) Math. Comp. , vol.44 , pp. 105-124
    • Parlett, B.N.1    Taylor, D.R.2    Liu, Z.S.3
  • 141
    • 0002058827 scopus 로고
    • The numerical solution of elliptic and parabolic differential equations
    • Peaceman D., Rachford H. The numerical solution of elliptic and parabolic differential equations. J. SIAM. 3:1955;28-41.
    • (1955) J. SIAM , vol.3 , pp. 28-41
    • Peaceman, D.1    Rachford, H.2
  • 143
    • 0024961178 scopus 로고
    • Parallel conjugate gradient-like algorithms for solving sparse nonsymmetric systems on a vector multiprocessor
    • Radicati di Brozolo G., Robert Y. Parallel conjugate gradient-like algorithms for solving sparse nonsymmetric systems on a vector multiprocessor. Parallel Comput. 11:1989;223-239.
    • (1989) Parallel Comput. , vol.11 , pp. 223-239
    • Radicati Di Brozolo, G.1    Robert, Y.2
  • 144
    • 0039879187 scopus 로고
    • On the convergence of the classical iterative method of solving linear simultaneous equations
    • Reich E. On the convergence of the classical iterative method of solving linear simultaneous equations. Ann. Math. Statist. 20:1949;448-451.
    • (1949) Ann. Math. Statist. , vol.20 , pp. 448-451
    • Reich, E.1
  • 145
    • 0002655630 scopus 로고
    • On the method of conjugate gradients for the solution of large sparse systems of linear equations
    • J.K. Reid. New York: Academic Press
    • Reid J.K. On the method of conjugate gradients for the solution of large sparse systems of linear equations. Reid J.K. Large Sparse Sets of Linear Equations. 1971;231-254 Academic Press, New York.
    • (1971) Large Sparse Sets of Linear Equations , pp. 231-254
    • Reid, J.K.1
  • 146
    • 0000170864 scopus 로고
    • The approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to the stresses to 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 to a masonry dam. Philos. Trans. Roy. Soc. London Ser. A. 210:1910;307-357.
    • (1910) Philos. Trans. Roy. Soc. London Ser. a , vol.210 , pp. 307-357
    • Richardson, L.F.1
  • 147
    • 0040901834 scopus 로고
    • Contraction en norme vectorielle: Convergence d'itérations chaotiques
    • Robert F. Contraction en norme vectorielle: convergence d'itérations chaotiques. Linear Algebra Appl. 13:1976;19-35.
    • (1976) Linear Algebra Appl. , vol.13 , pp. 19-35
    • Robert, F.1
  • 148
    • 0010072149 scopus 로고
    • Iterations chaotiques série-parallèle pour les équations non linéaires de point fixe
    • Robert F., Charnay M., Musy F. Iterations chaotiques série-parallèle pour les équations non linéaires de point fixe. Apl. Math. 20:1975;1-38.
    • (1975) Apl. Math. , vol.20 , pp. 1-38
    • Robert, F.1    Charnay, M.2    Musy, F.3
  • 151
    • 0001249889 scopus 로고
    • Practical use of polynomial preconditionings for the conjugate gradient method
    • Saad Y. Practical use of polynomial preconditionings for the conjugate gradient method. SIAM J. Sci. Statist. Comput. 6:1985;865-881.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 865-881
    • Saad, Y.1
  • 152
    • 0023288135 scopus 로고
    • Least squares polynomials in the complex plane and their use for solving sparse nonsymmetric linear systems
    • Saad Y. Least squares polynomials in the complex plane and their use for solving sparse nonsymmetric linear systems. SIAM J. Numer. Anal. 24:1987;155-169.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 155-169
    • Saad, Y.1
  • 153
    • 0002598644 scopus 로고
    • Preconditioning techniques for indefinite and nonsymmetric linear systems
    • Saad Y. Preconditioning techniques for indefinite and nonsymmetric linear systems. J. Comput. Appl. Math. 24:1988;89-105.
    • (1988) J. Comput. Appl. Math. , vol.24 , pp. 89-105
    • Saad, Y.1
  • 154
    • 0001609443 scopus 로고
    • Krylov subspace methods on supercomputers
    • Saad Y. Krylov subspace methods on supercomputers. SIAM J. Sci. Statist. Comput. 10:1989;1200-1232.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 1200-1232
    • Saad, Y.1
  • 155
    • 0000954680 scopus 로고
    • A flexible inner-outer preconditioned GMRES algorithm
    • Saad Y. A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Statist. Comput. 14:1993;461-469.
    • (1993) SIAM J. Sci. Statist. Comput. , vol.14 , pp. 461-469
    • Saad, Y.1
  • 158
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving a nonsymmetric linear systems
    • Saad Y., Schultz M.H. GMRES: a generalized minimal residual algorithm for solving a nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7:1986;856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 160
    • 0039287302 scopus 로고
    • Computing the roots of complex orthogonal kernel polynomials
    • Saylor P.E., Smolarski D.C. Computing the roots of complex orthogonal kernel polynomials. SIAM J. Sci. Statist. Comput. 9:1988;1-13.
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 1-13
    • Saylor, P.E.1    Smolarski, D.C.2
  • 161
    • 84968487134 scopus 로고
    • On the numerical solution of elliptic difference equations
    • Sheldon J.W. On the numerical solution of elliptic difference equations. MTAC. 9:1955;101-112.
    • (1955) MTAC , vol.9 , pp. 101-112
    • Sheldon, J.W.1
  • 162
    • 0039879180 scopus 로고
    • Use of Tschebyscheff-polynomial operators in the solution of boundary value problems
    • Shortley G.H. Use of Tschebyscheff-polynomial operators in the solution of boundary value problems. J. Appl. Phys. 24:1953;392-396.
    • (1953) J. Appl. Phys. , vol.24 , pp. 392-396
    • Shortley, G.H.1
  • 163
    • 0039879182 scopus 로고
    • Incomplete LU preconditioners for conjugate gradient type iterative methods
    • Dallas, TX, Society of Petroleum Engineers of AIME, Paper No 13533
    • H.D. Simon, Incomplete LU preconditioners for conjugate gradient type iterative methods, in: Proceedings of the SPE 1985 Reservoir Simulation Symposium, Dallas, TX, Society of Petroleum Engineers of AIME, Paper No 13533, 1988, pp. 302-306.
    • (1988) In: Proceedings of the SPE 1985 Reservoir Simulation Symposium , pp. 302-306
    • Simon, H.D.1
  • 165
    • 0001845470 scopus 로고
    • BICGSTAB( ℓ ) for linear equations involving unsymmetric matrices with complex spectrum
    • Sleijpen G.L.G., Fokkema D.R. BICGSTAB(. ℓ ) for linear equations involving unsymmetric matrices with complex spectrum ETNA. 1:1993;11-32.
    • (1993) ETNA , vol.1 , pp. 11-32
    • Sleijpen, G.L.G.1    Fokkema, D.R.2
  • 166
    • 0002716979 scopus 로고
    • CGS: A fast Lanczos-type solver for nonsymmetric linear systems
    • Sonnoveld P. CGS: a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 10:1989;36-52.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 36-52
    • Sonnoveld, P.1
  • 167
    • 0002466742 scopus 로고
    • Stress calculation in frameworks by the method of systematic relaxation of constraints
    • Southwell R.V. Stress calculation in frameworks by the method of systematic relaxation of constraints. Proc. Roy. Soc. London Ser. A. 151:1935;56-95.
    • (1935) Proc. Roy. Soc. London Ser. a , vol.151 , pp. 56-95
    • Southwell, R.V.1
  • 168
    • 0023755844 scopus 로고
    • Imaging algorithms, accuracy and resolution in delay time tomography
    • in: N.J. Vlaar, N. Nolet, M. Wortel, S. Cloetingh (Eds.) Reidel, Dordrecht
    • W. Spakman, G. Nolet, Imaging algorithms, accuracy and resolution in delay time tomography, in: N.J. Vlaar, N. Nolet, M. Wortel, S. Cloetingh (Eds.), Mathematical Geophysics: A Survey of Recent Developments in Seismology and Geodynamics, Reidel, Dordrecht, 1987, pp. 155-188.
    • (1987) Mathematical Geophysics: A Survey of Recent Developments in Seismology and Geodynamics , pp. 155-188
    • Spakman, W.1    Nolet, G.2
  • 169
    • 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. 23:1948;111-118.
    • (1948) J. London Math. Soc. , vol.23 , pp. 111-118
    • Stein, P.1    Rosenberg, R.L.2
  • 170
    • 0002115888 scopus 로고
    • Kernel polynomials in linear algebra and their applications
    • Stiefel E.L. Kernel polynomials in linear algebra and their applications. U.S. Nat. Bur. Standards Appl. Math. Ser. 49:1958;1-24.
    • (1958) U.S. Nat. Bur. Standards Appl. Math. Ser. , vol.49 , pp. 1-24
    • Stiefel, E.L.1
  • 171
    • 0000564676 scopus 로고
    • Iterative solution of implicit approximations of multidimensional partial differential equations
    • Stone H.L. Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J. Numer. Anal. 5:1968;530-558.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 530-558
    • Stone, H.L.1
  • 172
    • 0000685145 scopus 로고
    • On the real convergence rate of the conjugate gradient method
    • Strakoš Z. On the real convergence rate of the conjugate gradient method. Linear Algebra Appl. 154 / 156:1991;535-549.
    • (1991) Linear Algebra Appl. , vol.154-156 , pp. 535-549
    • Strakoš, Z.1
  • 173
  • 174
    • 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. 17:1971;203-214.
    • (1971) Numer. Math. , vol.17 , pp. 203-214
    • Tanabe, K.1
  • 175
  • 179
    • 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. 48:1986;543-560.
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • Van Der Sluis, A.1    Van Der Vorst, H.A.2
  • 180
    • 0000298534 scopus 로고
    • The problem of a non-selfadjoint generalization of the conjugate gradient method has been closed
    • Voevodin V.V. The problem of a non-selfadjoint generalization of the conjugate gradient method has been closed. USSR Comput. Math. Math. Phys. 23:1983;143-144.
    • (1983) USSR Comput. Math. Math. Phys. , vol.23 , pp. 143-144
    • Voevodin, V.V.1
  • 181
    • 0002003127 scopus 로고
    • Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems
    • van der Vorst H.A. Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems. J. Comput. Phys. 44:1981;1-19.
    • (1981) J. Comput. Phys. , vol.44 , pp. 1-19
    • Van Der Vorst, H.A.1
  • 182
  • 183
    • 0022750329 scopus 로고
    • Large tridiagonal and block tridiagonal linear systems on vector and parallel computers
    • van der Vorst H.A. Large tridiagonal and block tridiagonal linear systems on vector and parallel computers. Parallel Comput. 5:1987;45-54.
    • (1987) Parallel Comput. , vol.5 , pp. 45-54
    • Van Der Vorst, H.A.1
  • 185
    • 0024665617 scopus 로고
    • ICCG and related method for 3-D problems on vector computers
    • in: D. Truhlar (Ed.), Workshop on Practical Iterative Methods for Large Scale Computations, Minneaopolis, MN, October 23-25
    • H.A. van der Vorst, ICCG and related method for 3-D problems on vector computers, in: D. Truhlar (Ed.), Workshop on Practical Iterative Methods for Large Scale Computations, Minneaopolis, MN, October 23-25, 1988, Comput. Phys. Comm. 53 (1989).
    • (1988) Comput. Phys. Comm. , vol.53
    • Van Der Vorst, H.A.1
  • 186
    • 0000005482 scopus 로고
    • Bi-CDSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems
    • van der Vorst H.A. Bi-CDSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Statist. Comput. 13:1992;631-644.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 189
    • 0002340103 scopus 로고
    • Factorization and normalized iterative methods
    • R.E. Langer. Madison: University of Wisconsin Press
    • Varga R.S. Factorization and normalized iterative methods. Langer R.E. Boundary Problems in Differential Equations. 1960;121-142 University of Wisconsin Press, Madison.
    • (1960) Boundary Problems in Differential Equations , pp. 121-142
    • Varga, R.S.1
  • 190
    • 0016873451 scopus 로고
    • ORTHOMIN: an iterative method solving sparse sets of simultaneous linear equations
    • Society of Petroleum Engineers of AIME
    • P.K.W. Vinsome, ORTHOMIN: an iterative method solving sparse sets of simultaneous linear equations, Proceedings of the Fourth Symposium on Reservoir Simulation, Society of Petroleum Engineers of AIME, 1976, pp. 149-159.
    • (1976) Proceedings of the Fourth Symposium on Reservoir Simulation , pp. 149-159
    • Vinsome, P.K.W.1
  • 191
  • 194
    • 84985384572 scopus 로고
    • Parallel block preconditioning based on SSOR and MILU
    • Washio T., Hayami K. Parallel block preconditioning based on SSOR and MILU. Numer. Linear Algebra Appl. 1:1994;533-553.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 533-553
    • Washio, T.1    Hayami, K.2
  • 195
    • 0019359208 scopus 로고
    • A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation
    • Watts III J.W. A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation. Soc. Petroleum Eng. J. 21:1981;345-353.
    • (1981) Soc. Petroleum Eng. J. , vol.21 , pp. 345-353
    • Watts J.W. III1
  • 196
    • 0001044969 scopus 로고
    • Error-minimixing Krylov subspace methods
    • Weiss R. Error-minimixing Krylov subspace methods. SIAM J. Sci. Comput. 15:1994;511-527.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 511-527
    • Weiss, R.1
  • 200
    • 0011053371 scopus 로고
    • A Lanczos method for a class of nonsymmetric systems of linear equations
    • Widlund O. A Lanczos method for a class of nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 15:1978;801-812.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 801-812
    • Widlund, O.1
  • 204
    • 85162695718 scopus 로고
    • On Richardson's method for solving linear systems with positive definite matrices
    • Young D.M. On Richardson's method for solving linear systems with positive definite matrices. J. Math. Phys. 32:1954;243-255.
    • (1954) J. Math. Phys. , vol.32 , pp. 243-255
    • Young, D.M.1
  • 207
    • 0031082725 scopus 로고    scopus 로고
    • GPBi-CG: Generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems
    • Zhang S.-L. GPBi-CG: generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems. SIAM J. Sci. Comput. 18:1997;537-551.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 537-551
    • Zhang, S.-L.1
  • 208
    • 0001481227 scopus 로고
    • Use of iterative refinement in the solution of sparse linear systems
    • Zlatev Z. Use of iterative refinement in the solution of sparse linear systems. SIAM J. Numer. Anal. 19:1982;381-399.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 381-399
    • Zlatev, Z.1


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