메뉴 건너뛰기




Volumn 9, Issue 4, 2002, Pages 371-402

Explicit approximate inverse preconditioning techniques

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL COMPLEXITY; EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0036989839     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03041466     Document Type: Review
Times cited : (50)

References (141)
  • 3
    • 0013252548 scopus 로고
    • Finite element solution of boundary value problems
    • Academic Press
    • Axelsson O. and Barker A. (1984). Finite element solution of boundary value problems. Theory and computation, Academic Press.
    • (1984) Theory and Computation
    • Axelsson, O.1    Barker, A.2
  • 4
    • 0024941111 scopus 로고
    • On a class of preconditioned iterative methods for parallel computers
    • Axelsson O., Carey G.F. and Lindskog G. (1989). On a class of preconditioned iterative methods for parallel computers. Inter. J. Numer. Meth. Eng., 27, 637-654.
    • (1989) Inter. J. Numer. Meth. Eng. , vol.27 , pp. 637-654
    • Axelsson, O.1    Carey, G.F.2    Lindskog, G.3
  • 5
    • 0001276831 scopus 로고
    • On the eigenvalue distribution of a class of preconditioning matrices
    • Axelsson O. and Lindskog G. (1986). On the eigenvalue distribution of a class of preconditioning matrices. Numer. Math., 48, 479-498.
    • (1986) Numer. Math. , vol.48 , pp. 479-498
    • Axelsson, O.1    Lindskog, G.2
  • 7
    • 0013239905 scopus 로고
    • Some numerical experiments using Newton's method for non-linear parabolic and elliptic boundary value problems
    • Belman R., Juncosa M.L. and Kalaba R. (1961). Some numerical experiments using Newton's method for non-linear parabolic and elliptic boundary value problems. C.A.C.M., 4, 187-191.
    • (1961) C.A.C.M. , vol.4 , pp. 187-191
    • Belman, R.1    Juncosa, M.L.2    Kalaba, R.3
  • 8
    • 0004675411 scopus 로고    scopus 로고
    • A sparse approximate inverse preconditioner for the conjugate gradient method
    • Benzi M., Meyer C.D. and Tuma M. (1996). A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput., 17, 1135-1149.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 1135-1149
    • Benzi, M.1    Meyer, C.D.2    Tuma, M.3
  • 10
    • 84966211313 scopus 로고
    • The construction of Preconditioners for elliptic problems by Substructuring II
    • Bramble J.H., Pasciak J.E. and Schatz A.H. (1988). The construction of Preconditioners for elliptic problems by Substructuring II. Math Comp., 51, 415-430.
    • (1988) Math Comp. , vol.51 , pp. 415-430
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 11
    • 84966199070 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring I
    • Bramble J.H., Pasciak J.G. and Schatz A.H. (1986). The construction of preconditioners for elliptic problems by substructuring I. Math. Comp., 47. 103-134.
    • (1986) Math. Comp. , vol.47 , pp. 103-134
    • Bramble, J.H.1    Pasciak, J.G.2    Schatz, A.H.3
  • 12
    • 84966238014 scopus 로고
    • An iterative method for elliptic problems on regions partitioned in substructures
    • Bramble J.H., Pasciak J.G. and Schatz A.H. (1986). An iterative method for elliptic problems on regions partitioned in substructures. Math. Comp., 46, 361-369.
    • (1986) Math. Comp. , vol.46 , pp. 361-369
    • Bramble, J.H.1    Pasciak, J.G.2    Schatz, A.H.3
  • 13
    • 0000713765 scopus 로고
    • Row projection methods for large nonsymmetric linear systems
    • Bramley R. and Sameh A. (1992). Row projection methods for large nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 13, 168-193.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 168-193
    • Bramley, R.1    Sameh, A.2
  • 14
    • 0001045889 scopus 로고
    • A numerical method for the solution of two-dimensional and three dimensional equations of diffusion
    • Buleev N.I. (1960). A numerical method for the solution of two-dimensional and three dimensional equations of diffusion. Math. Sbornik, 51, 227-238.
    • (1960) Math. Sbornik , vol.51 , pp. 227-238
    • Buleev, N.I.1
  • 15
    • 84966252378 scopus 로고
    • On the stability of relaxed incomplete LU factorizations
    • Bruaset A.M., Tveito A. and Winther R. (1990). On the stability of relaxed incomplete LU factorizations. Math. Comp., 54. 701-719.
    • (1990) Math. Comp. , vol.54 , pp. 701-719
    • Bruaset, A.M.1    Tveito, A.2    Winther, R.3
  • 16
    • 0013240081 scopus 로고
    • A note on the efficiency of domain decomposed incomplete factorizations
    • Chan T.F. and Goovaerts D. (1990). A note on the efficiency of domain decomposed incomplete factorizations. SIAM J. Sci. Stat. Comput., 11, 794-803.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 794-803
    • Chan, T.F.1    Goovaerts, D.2
  • 17
    • 0023331179 scopus 로고
    • Analysis of preconditioners for domain decomposition
    • Chan T.F. (1987). Analysis of preconditioners for domain decomposition. SIAM J. Num. Anal. 24, 382-390.
    • (1987) SIAM J. Num. Anal. , vol.24 , pp. 382-390
    • Chan, T.F.1
  • 19
    • 84974325009 scopus 로고
    • Domain decomposition algorithms
    • Chan T.F. and Mathew T. (1994). Domain decomposition algorithms. Acta Numerica, 61-144.
    • (1994) Acta Numerica , pp. 61-144
    • Chan, T.F.1    Mathew, T.2
  • 20
    • 0002457199 scopus 로고
    • Approximate inverse preconditioning for sparse linear systems
    • Cosgrove J.D.F., Dias J.C. and Griewank A. (1992). Approximate inverse preconditioning for sparse linear systems. Inter. J. Comp. Math., 44, 91-110.
    • (1992) Inter. J. Comp. Math. , vol.44 , pp. 91-110
    • Cosgrove, J.D.F.1    Dias, J.C.2    Griewank, A.3
  • 23
  • 24
  • 25
    • 0013189220 scopus 로고
    • Performance of various computers using standard sparse linear equations solving techniques
    • Dongarra J. and van der Vorst H. (1992). Performance of various computers using standard sparse linear equations solving techniques. Supercomputer, 9(5), 17-29.
    • (1992) Supercomputer , vol.9 , Issue.5 , pp. 17-29
    • Dongarra, J.1    Van der Vorst, H.2
  • 26
    • 0000530612 scopus 로고
    • A finite element capacitance method for elliptic problems on regions partitioned into subregions
    • Dryja M. (1984). A finite element capacitance method for elliptic problems on regions partitioned into subregions. Num. Math., 44, 153-168.
    • (1984) Num. Math. , vol.44 , pp. 153-168
    • Dryja, M.1
  • 27
    • 0001954099 scopus 로고
    • A capacitance matrix method for Dirichlet problem on polygonal region
    • Dryja M. (1982). A capacitance matrix method for Dirichlet problem on polygonal region. Num. Math., 39, 51-64.
    • (1982) Num. Math. , vol.39 , pp. 51-64
    • Dryja, M.1
  • 28
    • 0018707156 scopus 로고
    • Approximating the inverse of a matrix for use in iterative algorithms on vector processors
    • Dubois P., Greenbaum A. and Rodrigue G. (1979). Approximating the inverse of a matrix for use in iterative algorithms on vector processors. Computing, 22, 257-268.
    • (1979) Computing , vol.22 , pp. 257-268
    • Dubois, P.1    Greenbaum, A.2    Rodrigue, G.3
  • 29
    • 0034319806 scopus 로고    scopus 로고
    • The impact of high performance computing in the solution of linear systems: Trends and problems
    • Duff I. (2000). The impact of high performance computing in the solution of linear systems : trends and problems. J. Comp. Applied Math., 123, 515-530.
    • (2000) J. Comp. Applied Math. , vol.123 , pp. 515-530
    • Duff, I.1
  • 31
    • 0000762041 scopus 로고
    • An approximate factorization procedure for solving self-adjoint elliptic difference equations
    • Dupont T., Kendall R. and Rachford H. (1968). An approximate factorization procedure for solving self-adjoint elliptic difference equations. SIAM J. Numer. Anal., 5, 559-573.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 559-573
    • Dupont, T.1    Kendall, R.2    Rachford, H.3
  • 32
    • 0013240557 scopus 로고
    • A note on the generalized conjugate gradient method
    • Eisenstat S.C. (1983). A note on the generalized conjugate gradient method. SIAM J. Numer. Anal., 20, 358-361.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 358-361
    • Eisenstat, S.C.1
  • 33
    • 0001330133 scopus 로고
    • Relaxed and stabilized incomplete factorization for non-self-adjoint linear systems
    • Elman H.C. (1989). Relaxed and stabilized incomplete factorization for non-self-adjoint linear systems. BIT, 29, 890-915.
    • (1989) BIT , vol.29 , pp. 890-915
    • Elman, H.C.1
  • 34
    • 84966211825 scopus 로고
    • A stability analysis of incomplete LU factorizations
    • Elman H.C. (1986). A stability analysis of incomplete LU factorizations. Math. Comp., 47, 191-217.
    • (1986) Math. Comp. , vol.47 , pp. 191-217
    • Elman, H.C.1
  • 37
    • 0000234821 scopus 로고
    • The use of Preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices
    • Evans, D.J. (1967). The use of Preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices. J.I.M.A., 4, 295-314.
    • (1967) J.I.M.A. , vol.4 , pp. 295-314
    • Evans, D.J.1
  • 38
    • 0021004231 scopus 로고
    • Implicit semi-direct methods based on root-free sparse factorization procedures
    • Evans D.J. and Lipitakis E.A. (1983). Implicit semi-direct methods based on root-free sparse factorization procedures. BIT, 23, 194-208.
    • (1983) BIT , vol.23 , pp. 194-208
    • Evans, D.J.1    Lipitakis, E.A.2
  • 40
    • 0021416130 scopus 로고
    • Necessary and sufficient conditions for the existence of a conjugate gradient method
    • Faber V. and Manteuffel T. (1984). Necessary and sufficient conditions for the existence of a conjugate gradient method. SIAM J. Numer. Anal., 21, 315-339.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 315-339
    • Faber, V.1    Manteuffel, T.2
  • 42
    • 84966211417 scopus 로고
    • On Fourier-Toeplitz methods for separable elliptic problems
    • Fisher D., Golub G., Hald O., Leiva C. and Widlund O. (1974). On Fourier-Toeplitz methods for separable elliptic problems. Math Comp., 28, 349-368.
    • (1974) Math Comp. , vol.28 , pp. 349-368
    • Fisher, D.1    Golub, G.2    Hald, O.3    Leiva, C.4    Widlund, O.5
  • 44
    • 0010048239 scopus 로고
    • Domain decomposition methods for partial differential equations
    • Glowinski R., Golub G. H., Meurant G. A. and Periaux J. (1988). Domain Decomposition Methods for Partial Differential Equations. SIAM.
    • (1988) SIAM
    • Glowinski, R.1    Golub, G.H.2    Meurant, G.A.3    Periaux, J.4
  • 46
    • 0024631560 scopus 로고
    • Some history of the conjugate gradient and lanczos algorithms: 1948-1976
    • Golub G.H. and O'Leary D.P. (1989). Some history of the conjugate gradient and lanczos algorithms: 1948-1976. SIAM Review, 31, 50-102.
    • (1989) SIAM Review , vol.31 , pp. 50-102
    • Golub, G.H.1    O'Leary, D.P.2
  • 47
    • 0001190030 scopus 로고
    • The numerically stable reconstruction of Jacobi matrix from spectral data
    • Gragg B. and Harrod W. (1984). The numerically stable reconstruction of Jacobi matrix from spectral data. Numer. Math., 44, 317-355.
    • (1984) Numer. Math. , vol.44 , pp. 317-355
    • Gragg, B.1    Harrod, W.2
  • 48
    • 0013189624 scopus 로고    scopus 로고
    • A note on the rate of convergence and complexity of domain decomposition approximate inverse preconditioning
    • Computational Fluid and Solid Mechanics, eds. K.J. Bathe. Elsevier
    • Gravvanis G.A. (2001). A note on the rate of convergence and complexity of domain decomposition approximate inverse preconditioning. Computational Fluid and Solid Mechanics, Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, eds. K.J. Bathe. Vol 2, Elsevier, 1586-1589.
    • (2001) Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics , vol.2 , pp. 1586-1589
    • Gravvanis, G.A.1
  • 50
    • 0013241810 scopus 로고    scopus 로고
    • Explicit preconditioned generalized domain decomposition methods
    • Gravvanis G.A. (2000). Explicit preconditioned generalized domain decomposition methods. I. J. Applied Mathematics, 4(1), 57-71.
    • (2000) I. J. Applied Mathematics , vol.4 , Issue.1 , pp. 57-71
    • Gravvanis, G.A.1
  • 53
    • 0013189223 scopus 로고    scopus 로고
    • Fast explicit approximate inverses for solving linear and non-linear finite difference equations
    • Gravvanis G.A. (2000). Fast explicit approximate inverses for solving linear and non-linear finite difference equations. I. J. Differential Equations & Applications, 1(4), 451-473.
    • (2000) I. J. Differential Equations & Applications , vol.1 , Issue.4 , pp. 451-473
    • Gravvanis, G.A.1
  • 54
    • 0013251505 scopus 로고    scopus 로고
    • Generalized approximate inverse preconditioning for solving non-linear elliptic boundary-value problems
    • Gravvanis G.A. (2000). Generalized approximate inverse preconditioning for solving non-linear elliptic boundary-value problems. I. J. Applied Mathematics, 2(11). 1363-1378.
    • (2000) I. J. Applied Mathematics , vol.2 , Issue.11 , pp. 1363-1378
    • Gravvanis, G.A.1
  • 55
    • 0013252553 scopus 로고    scopus 로고
    • Domain decomposition approximate inverse matrix techniques
    • Gravvanis G.A. (2000). Domain decomposition approximate inverse matrix techniques. I. J. Differential Equations and Applications, 1(3), 323-334.
    • (2000) I. J. Differential Equations and Applications , vol.1 , Issue.3 , pp. 323-334
    • Gravvanis, G.A.1
  • 56
    • 2942558493 scopus 로고    scopus 로고
    • Using explicit preconditioned domain decomposition methods for solving singular perturbed linear problems
    • M. Ingber, H. Power, & C.A. Brebbia (Eds.), WIT Press
    • Gravvanis G.A. (2000). Using explicit preconditioned domain decomposition methods for solving singular perturbed linear problems. Applications of High Performance Computing in Engineering VI, M. Ingber, H. Power, & C.A. Brebbia (Eds.), WIT Press, 457-466.
    • (2000) Applications of High Performance Computing in Engineering VI , pp. 457-466
    • Gravvanis, G.A.1
  • 57
    • 0013255655 scopus 로고    scopus 로고
    • Explicit preconditioning conjugate gradient schemes for solving biharmonic problems
    • Gravvanis G.A. (2000). Explicit preconditioning conjugate gradient schemes for solving biharmonic problems. Engineering Computations, 17, 154-165.
    • (2000) Engineering Computations , vol.17 , pp. 154-165
    • Gravvanis, G.A.1
  • 58
    • 0033687123 scopus 로고    scopus 로고
    • Explicit isomorphic iterative methods for solving arrow-type linear systems
    • Gravvanis G.A. (2000). Explicit isomorphic iterative methods for solving arrow-type linear systems. I. J. Comp. Math., 74(2), 195-206.
    • (2000) I. J. Comp. Math. , vol.74 , Issue.2 , pp. 195-206
    • Gravvanis, G.A.1
  • 59
    • 0013188738 scopus 로고    scopus 로고
    • Generalized approximate inverse finite element matrix techniques
    • Gravvanis G.A. (1999). Generalized approximate inverse finite element matrix techniques. Neural Parallel and Scientific Computations, 7(4). 487-500.
    • (1999) Neural Parallel and Scientific Computations , vol.7 , Issue.4 , pp. 487-500
    • Gravvanis, G.A.1
  • 60
    • 0032625710 scopus 로고    scopus 로고
    • Approximate inverse banded matrix techniques
    • Gravvanis G.A. (1999). Approximate inverse banded matrix techniques. Engineering Computations, 16(3), 337-346.
    • (1999) Engineering Computations , vol.16 , Issue.3 , pp. 337-346
    • Gravvanis, G.A.1
  • 61
    • 0013303767 scopus 로고    scopus 로고
    • Preconditioned iterative methods for solving 3D boundary value problems
    • Gravvanis G.A. (1999). Preconditioned iterative methods for solving 3D boundary value problems. I. J. Comp. Math., 71, 117-136.
    • (1999) I. J. Comp. Math. , vol.71 , pp. 117-136
    • Gravvanis, G.A.1
  • 62
    • 0002398607 scopus 로고    scopus 로고
    • An approximate inverse matrix technique for arrowhead matrices
    • Gravvanis G.A. (1998). An approximate inverse matrix technique for arrowhead matrices. I. J. Comp. Math., 70, 35-45.
    • (1998) I. J. Comp. Math. , vol.70 , pp. 35-45
    • Gravvanis, G.A.1
  • 63
    • 0013255139 scopus 로고    scopus 로고
    • Parallel matrix techniques
    • K.D. Papailiou, D. Tsahalis, J. Periaux, C. Hirsch, M. Pandolfi (Eds.), Wiley
    • Gravvanis G.A. (1998). Parallel matrix techniques. Computational Fluid Dynamics 98, K.D. Papailiou, D. Tsahalis, J. Periaux, C. Hirsch, M. Pandolfi (Eds.), Vol. I, Part 1, Wiley, 472-477.
    • (1998) Computational Fluid Dynamics 98 , vol.1 , Issue.PART 1 , pp. 472-477
    • Gravvanis, G.A.1
  • 64
    • 0000259855 scopus 로고    scopus 로고
    • Solving non-linear boundary value problems in three dimensions by explicit preconditioning
    • R. Van Keer, B. Verhegghe, M. Hogge, E. Noldus (Eds.). Part 2: Contributed Papers, Shaker Publishing
    • Gravvanis G.A. (1998). Solving non-linear boundary value problems in three dimensions by explicit preconditioning. Proceedings of the International Conference on Advanced Computational Methods in Engineering, R. Van Keer, B. Verhegghe, M. Hogge, E. Noldus (Eds.). Part 2: Contributed Papers, Shaker Publishing, 755-762.
    • (1998) Proceedings of the International Conference on Advanced Computational Methods in Engineering , pp. 755-762
    • Gravvanis, G.A.1
  • 65
    • 0000874034 scopus 로고    scopus 로고
    • On the numerical modelling and solution of non-linear boundary value problems
    • R. W. Lewis and J.T. Cross (Eds.), Vol X, Pineridge Press
    • Gravvanis G.A. (1997). On the numerical modelling and solution of non-linear boundary value problems. Numerical Methods in Thermal Problems. R. W. Lewis and J.T. Cross (Eds.), Vol X, Pineridge Press, 898-909.
    • (1997) Numerical Methods in Thermal Problems , vol.10 , pp. 898-909
    • Gravvanis, G.A.1
  • 66
    • 0029777947 scopus 로고    scopus 로고
    • The rate of convergence of explicit approximate inverse preconditioning
    • Gravvanis G.A. (1996). The rate of convergence of explicit approximate inverse preconditioning. I. J. Comp. Math., 60, 77-89.
    • (1996) I. J. Comp. Math. , vol.60 , pp. 77-89
    • Gravvanis, G.A.1
  • 67
    • 0029541853 scopus 로고
    • Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques
    • Gravvanis G.A. (1995). Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques. I. J. Comp. Math., 56, 77-93.
    • (1995) I. J. Comp. Math. , vol.56 , pp. 77-93
    • Gravvanis, G.A.1
  • 70
    • 0030194147 scopus 로고    scopus 로고
    • A three dimensional explicit preconditioned solver
    • Gravvanis G.A. and Lipitakis E.A. (1996). A three dimensional explicit preconditioned solver. Comp. Math. with Appl., 32, 111-131.
    • (1996) Comp. Math. with Appl. , vol.32 , pp. 111-131
    • Gravvanis, G.A.1    Lipitakis, E.A.2
  • 71
    • 0013190389 scopus 로고
    • On the numerical modelling and solution of initial/boundary value problems
    • Lewis R.W. and Durbetaki P. (Eds.). Pineridge Press
    • Gravvanis G.A. and Lipitakis E.A. (1995). On the numerical modelling and solution of initial/boundary value problems. Proc. of the 9th Inter. Conference on Numerical Methods in Thermal Problems, Lewis R.W. and Durbetaki P. (Eds.). Vol. IX, Part 2, Pineridge Press, 782-793.
    • (1995) Proc. of the 9th Inter. Conference on Numerical Methods in Thermal Problems , vol.9 , Issue.PART 2 , pp. 782-793
    • Gravvanis, G.A.1    Lipitakis, E.A.2
  • 72
    • 0013189955 scopus 로고
    • Using generalized approximate inverse finite element methods for the numerical solution of initial/boundary value problems
    • E.A. Lipitakis (Ed.), Hellenic Mathematical Society
    • Gravvanis G.A. and Lipitakis E.A. (1994). Using generalized approximate inverse finite element methods for the numerical solution of initial/boundary value problems. Proceedings of the Second Hellenic-European Conference on Mathematics and Informatics, E.A. Lipitakis (Ed.), Vol. 2, 829-838, Hellenic Mathematical Society.
    • (1994) Proceedings of the Second Hellenic-European Conference on Mathematics and Informatics , vol.2 , pp. 829-838
    • Gravvanis, G.A.1    Lipitakis, E.A.2
  • 74
    • 0003347655 scopus 로고    scopus 로고
    • Iterative methods for solving linear systems
    • Greenbaum A. (1997). Iterative methods for solving linear systems. SIAM.
    • (1997) SIAM
    • Greenbaum, A.1
  • 75
    • 0001397416 scopus 로고
    • Domain decomposition with local mesh refinement
    • Gropp W.D. and Keyes D.E. (1992). Domain decomposition with local mesh refinement. SIAM J. Sci. Statist. Comput., 13, 967-993.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 967-993
    • Gropp, W.D.1    Keyes, D.E.2
  • 76
    • 0031129197 scopus 로고    scopus 로고
    • Parallel preconditioning with sparse approximate inverses
    • Grote M.J. and Huckle T. (1997). Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput., 18, 838-853.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 838-853
    • Grote, M.J.1    Huckle, T.2
  • 77
    • 0003039594 scopus 로고
    • A class of first order factorization methods
    • Gustafsson I. (1978). A class of first order factorization methods. BIT, 18, 142-156.
    • (1978) BIT , vol.18 , pp. 142-156
    • Gustafsson, I.1
  • 78
    • 0000846539 scopus 로고
    • Variants of BICGSTAB for matrices with complex spectrum
    • Gutknecht M.H. (1993). Variants of BICGSTAB for matrices with complex spectrum. SIAM J. Sci. Comput., 14, 1020-1033.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1020-1033
    • Gutknecht, M.H.1
  • 81
    • 0016423894 scopus 로고
    • Pseudoinverses and Conjugate gradients
    • Hestenes M.R. (1975). Pseudoinverses and Conjugate gradients. Commun. of A.C.M., 18, 40-43.
    • (1975) Commun. of A.C.M. , vol.18 , pp. 40-43
    • Hestenes, M.R.1
  • 82
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes M.R. and Stiefel E. (1954). Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand., 49, 409-436.
    • (1954) J. Res. Natl. Bur. Stand. , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 83
    • 0033149565 scopus 로고    scopus 로고
    • Approximate sparsity patterns for the inverse of a matrix and preconditioning
    • Huckle T. (1999). Approximate sparsity patterns for the inverse of a matrix and preconditioning. Applied Numerical Mathematics, 30, 291-303.
    • (1999) Applied Numerical Mathematics , vol.30 , pp. 291-303
    • Huckle, T.1
  • 84
    • 0032385045 scopus 로고    scopus 로고
    • Efficient computations of sparse approximate inverses
    • Huckle T. (1998). Efficient computations of sparse approximate inverses. Numer. Linear Alg. with Appl., 5, 57-71.
    • (1998) Numer. Linear Alg. with Appl. , vol.5 , pp. 57-71
    • Huckle, T.1
  • 85
    • 0001010277 scopus 로고
    • Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
    • Jea K. and Young D. (1980). Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods. Linear Algebra Appl., 34, 159-194.
    • (1980) Linear Algebra Appl. , vol.34 , pp. 159-194
    • Jea, K.1    Young, D.2
  • 86
    • 84985376638 scopus 로고
    • New convergence results and preconditioning strategies for the conjugate gradient method
    • Kaporin I. (1994). New convergence results and preconditioning strategies for the conjugate gradient method. Numer. Linear Alg. Appl., 1, 179-210.
    • (1994) Numer. Linear Alg. Appl. , vol.1 , pp. 179-210
    • Kaporin, I.1
  • 89
    • 21144474663 scopus 로고
    • Factorized sparse approximate inverse preconditioning
    • Kolotilina L.Y. and Yeremin A.Y. (1993). Factorized sparse approximate inverse preconditioning. SIAM J. Matrix Anal. Appl., 14, 45-58.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 45-58
    • Kolotilina, L.Y.1    Yeremin, A.Y.2
  • 90
    • 0002814189 scopus 로고
    • Solution of systems of linear equations by minimized iterations
    • Lanczos C. (1952). Solution of systems of linear equations by minimized iterations. J. Res. Natl. Bur. Stand, 49, 33-53.
    • (1952) J. Res. Natl. Bur. Stand , vol.49 , pp. 33-53
    • Lanczos, C.1
  • 91
    • 0000094593 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • Lanczos C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand, 45, 225-280.
    • (1950) J. Res. Natl. Bur. Stand , vol.45 , pp. 225-280
    • Lanczos, C.1
  • 92
    • 38249043664 scopus 로고
    • Approximate root-free factorization techniques for solving elliptic difference equations in three-space variables
    • Lipitakis E.A. (1986). Approximate root-free factorization techniques for solving elliptic difference equations in three-space variables. Linear Algebra and its Applications, 76, 247-269.
    • (1986) Linear Algebra and its Applications , vol.76 , pp. 247-269
    • Lipitakis, E.A.1
  • 93
    • 0021167819 scopus 로고
    • Generalized extended to the limit sparse factorization techniques for solving unsymmetric finite element systems
    • Lipitakis E.A. (1984). Generalized extended to the limit sparse factorization techniques for solving unsymmetric finite element systems. Computing, 32, 255-270.
    • (1984) Computing , vol.32 , pp. 255-270
    • Lipitakis, E.A.1
  • 94
    • 0020824239 scopus 로고
    • A normalized sparse linear equation solver
    • Lipitakis E.A. (1983). A normalized sparse linear equation solver. J. Comp. and Applied Maths, 9, 287-298.
    • (1983) J. Comp. and Applied Maths , vol.9 , pp. 287-298
    • Lipitakis, E.A.1
  • 95
    • 0023293305 scopus 로고
    • Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors
    • Lipitakis, E.A. and Evans D.J. (1987). Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors. Math. and Computers in Simulation, 29, 1-17.
    • (1987) Math. and Computers in Simulation , vol.29 , pp. 1-17
    • Lipitakis, E.A.1    Evans, D.J.2
  • 96
    • 0013255656 scopus 로고
    • Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods
    • Lipitakis, E.A. and Evans D.J. (1986). Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods. I. J. Comp. Math., 20, 261-282.
    • (1986) I. J. Comp. Math. , vol.20 , pp. 261-282
    • Lipitakis, E.A.1    Evans, D.J.2
  • 97
    • 0029220322 scopus 로고
    • Explicit preconditioned iterative methods for solving large unsymmetric finite element systems
    • Lipitakis E.A. and Gravvanis G.A. (1995). Explicit preconditioned iterative methods for solving large unsymmetric finite element systems. Computing, 54, 167-183.
    • (1995) Computing , vol.54 , pp. 167-183
    • Lipitakis, E.A.1    Gravvanis, G.A.2
  • 98
    • 0013291938 scopus 로고
    • Explicit preconditioned methods for computing the inverse and pseudoinverse solutions of unsymmetric finite element systems of linear equations
    • Lipitakis E.A. and Gravvanis G.A. (1994). Explicit preconditioned methods for computing the inverse and pseudoinverse solutions of unsymmetric finite element systems of linear equations. I. J. Mathematical Modelling and Scientific Computing, 4, 886-893.
    • (1994) I. J. Mathematical Modelling and Scientific Computing , vol.4 , pp. 886-893
    • Lipitakis, E.A.1    Gravvanis, G.A.2
  • 99
    • 0013187947 scopus 로고
    • Hybrid Implicit-Explicit schemes by approximate inverse finite element matrix techniques for solving parabolic partial differential equations
    • E.A. Lipitakis (Ed.), Hellenic Mathematical Society
    • Lipitakis E.A. and Gravvanis G.A. (1993). Hybrid Implicit-Explicit schemes by approximate inverse finite element matrix techniques for solving parabolic partial differential equations. Proceedings of the First Conference on Mathematics and Informatics, E.A. Lipitakis (Ed.), 345-356, Hellenic Mathematical Society.
    • (1993) Proceedings of the First Conference on Mathematics and Informatics , pp. 345-356
    • Lipitakis, E.A.1    Gravvanis, G.A.2
  • 100
    • 0013290992 scopus 로고
    • The use of explicit preconditioned iterative methods for solving singular perturbed linear problems
    • Hirsch C., Zienkiewicz O.C. and Onate E. (Eds.), Elsevier Science Publishers
    • Lipitakis E.A. and Gravvanis G.A. (1992). The use of explicit preconditioned iterative methods for solving singular perturbed linear problems. Numerical Methods in Engineering'92, Hirsch C., Zienkiewicz O.C. and Onate E. (Eds.), 827-832, Elsevier Science Publishers.
    • (1992) Numerical Methods in Engineering'92 , pp. 827-832
    • Lipitakis, E.A.1    Gravvanis, G.A.2
  • 102
    • 0013189629 scopus 로고
    • Implicit preconditioned methods based on root-free sparse finite element factorization techniques
    • Vichnevetsky, R. and Miller, J.J.H. (Eds.)
    • Lipitakis E.A. and Gravvanis G.A. (1991). Implicit preconditioned methods based on root-free sparse finite element factorization techniques. Proc. of the 13th IMACS World Congress on Computation and Applied Mathematics, Vichnevetsky, R. and Miller, J.J.H. (Eds.), Vol. 1, 449-450.
    • (1991) Proc. of the 13th IMACS World Congress on Computation and Applied Mathematics , vol.1 , pp. 449-450
    • Lipitakis, E.A.1    Gravvanis, G.A.2
  • 103
    • 0013301263 scopus 로고
    • A fast direct method for solving elliptic boundary value problems on multiprocessor systems
    • Pande, G.N. and Middleton, J. (Eds.), Elsevier Applied Science
    • Lipitakis E.A. and Gravvanis G.A. (1990). A fast direct method for solving elliptic boundary value problems on multiprocessor systems. Proc. of the Inter. Conf. on Numerical Methods in Engineering: Theory and Applications, Pande, G.N. and Middleton, J. (Eds.), Elsevier Applied Science, 622-632.
    • (1990) Proc. of the Inter. Conf. on Numerical Methods in Engineering: Theory and Applications , pp. 622-632
    • Lipitakis, E.A.1    Gravvanis, G.A.2
  • 104
    • 0001256129 scopus 로고
    • The Tchebychev iteration for nonsymmetric linear systems
    • Manteuffel T. (1977). The Tchebychev iteration for nonsymmetric linear systems. Numer. Math., 28, 307-327.
    • (1977) Numer. Math. , vol.28 , pp. 307-327
    • Manteuffel, T.1
  • 105
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • Meijerink J.A. and van der Vorst H.A. (1977). An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp., 31, 148-162.
    • (1977) Math. Comp. , vol.31 , pp. 148-162
    • Meijerink, J.A.1    Van der Vorst, H.A.2
  • 106
    • 84964127276 scopus 로고
    • Domain decomposition methods for partial differential equations on parallel computers
    • Meurant G. (1988). Domain decomposition methods for partial differential equations on parallel computers. Int. J. Supercomputing Appls., 2, 5-12.
    • (1988) Int. J. Supercomputing Appls. , vol.2 , pp. 5-12
    • Meurant, G.1
  • 107
    • 84976824344 scopus 로고
    • Solving sparse symmetric sets of linear equations by preconditioned conjugate gradients
    • Munksgaard N. (1980). Solving sparse symmetric sets of linear equations by preconditioned conjugate gradients. ACM Trans. Math. Software, 6, 206-219.
    • (1980) ACM Trans. Math. Software , vol.6 , pp. 206-219
    • Munksgaard, N.1
  • 109
    • 21144467170 scopus 로고
    • On the convergence rate of the conjugate gradients in presence of rounding errors
    • Notay Y. (1993). On the convergence rate of the conjugate gradients in presence of rounding errors. Numer. Math., 65, 301-317.
    • (1993) Numer. Math. , vol.65 , pp. 301-317
    • Notay, Y.1
  • 111
    • 38249017274 scopus 로고
    • Computing the eigenproblem and eigenvectors of arrowhead matrices
    • O'Leary D. and Stewart G. (1990). Computing the eigenproblem and eigenvectors of arrowhead matrices. J. Comp. Physics, 90, 497-505.
    • (1990) J. Comp. Physics , vol.90 , pp. 497-505
    • O'Leary, D.1    Stewart, G.2
  • 116
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • Peaceman D. and Rachford J.H.H. (1955). The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Math., 3, 28-41.
    • (1955) J. Soc. Indust. Appl. Math. , vol.3 , pp. 28-41
    • Peaceman, D.1    Rachford, J.H.H.2
  • 119
    • 0013303772 scopus 로고
    • On the origins and numerical solution of some sparse non-linear systems
    • Academic Press
    • Porsching T.A. (1976). On the origins and numerical solution of some sparse non-linear systems. In the book: "Sparse Matrix Computations", Academic Press.
    • (1976) Sparse Matrix Computations
    • Porsching, T.A.1
  • 121
    • 0002655630 scopus 로고
    • On the method of conjugate gradients for the solution of large sparse systems of linear equations
    • Reid J. (Ed.), Academic Press
    • Reid J. (1971). On the method of conjugate gradients for the solution of large sparse systems of linear equations. In Large Sparse Sets of Linear Equations, Reid J. (Ed.), Academic Press, 231-254.
    • (1971) Large Sparse Sets of Linear Equations , pp. 231-254
    • Reid, J.1
  • 123
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y. and Schultz M.H. (1986). GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 7, 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 124
    • 84966234359 scopus 로고
    • Conjugate Gradient-like algorithms for solving nonsymmetric linear systems
    • Saad Y. and Schultz M.H. (1985). Conjugate Gradient-like algorithms for solving nonsymmetric linear systems. Math. Comp., 44, 417-424.
    • (1985) Math. Comp. , vol.44 , pp. 417-424
    • Saad, Y.1    Schultz, M.H.2
  • 125
    • 0039179703 scopus 로고    scopus 로고
    • Iterative solution of linear systems in the 20th century
    • Saad Y. and van der Vorst H.A. (2000). Iterative solution of linear systems in the 20th century. J. Comp. Applied Math., 123, 1-33.
    • (2000) J. Comp. Applied Math. , vol.123 , pp. 1-33
    • Saad, Y.1    Van der Vorst, H.A.2
  • 127
    • 0000466442 scopus 로고
    • Maintaining convergence properties of BICGSTAB methods in finite precision arithmetic
    • Finite Element Methods
    • Sleijpen G.L.G. and van der Vorst H.A. (1995). Maintaining convergence properties of BICGSTAB methods in finite precision arithmetic. Numerical Algorithms, 10, 203-223. Finite Element Methods
    • (1995) Numerical Algorithms , vol.10 , pp. 203-223
    • Sleijpen, G.L.G.1    Van der Vorst, H.A.2
  • 128
    • 0001403122 scopus 로고
    • The rate of convergence of conjugate gradients
    • van der Sluis A. and van der Vorst H.A. (1986). The rate of convergence of conjugate gradients. Numer. Math., 48, 543-560.
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • Van der Sluis, A.1    Van der Vorst, H.A.2
  • 129
    • 0002716979 scopus 로고
    • CGS: A fast Lanczos-type solver for nonsymmetric linear systems
    • Sonneveld P. (1989). CGS: a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 10, 36-52.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 36-52
    • Sonneveld, P.1
  • 130
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems
    • van der Vorst H.A. (1992). Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Statist. Comput., 13, 631-644.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • Van der Vorst, H.A.1
  • 132
    • 0001259654 scopus 로고
    • A vectorizable variant of some ICCG methods
    • van der Vorst H.A. (1982). A vectorizable variant of some ICCG methods. SIAM J. Sci. Stat. Comput., 3, 350-356.
    • (1982) SIAM J. Sci. Stat. Comput. , vol.3 , pp. 350-356
    • Van der Vorst, H.A.1
  • 133
    • 84985336395 scopus 로고
    • GMRESR: A family of nested GMRES methods
    • van der Vorst H.A. and Vuik C. (1994). GMRESR: a family of nested GMRES methods. Numer. Linear Alg. Appl, 1(4), 369-386.
    • (1994) Numer. Linear Alg. Appl , vol.1 , Issue.4 , pp. 369-386
    • Van der Vorst, H.A.1    Vuik, C.2
  • 134
    • 0000388635 scopus 로고
    • A comparison of some GMRES-like methods
    • Vuik C. and van der Vorst H.A. (1992). A comparison of some GMRES-like methods. Linear Alg. Appl., 160, 131-162.
    • (1992) Linear Alg. Appl. , vol.160 , pp. 131-162
    • Vuik, C.1    Van der Vorst, H.A.2
  • 136
    • 0013290995 scopus 로고
    • Compact computation of the inverse of a matrix
    • Waugh F.V. and Dwyer P.S. (1945). Compact computation of the inverse of a matrix. Ann. Math. Stat., 16, 259-271.
    • (1945) Ann. Math. Stat. , vol.16 , pp. 259-271
    • Waugh, F.V.1    Dwyer, P.S.2
  • 137
    • 0013191213 scopus 로고
    • Some aspects of the mathematics of FE, in the Mathematics of FE and Applications II
    • Academic Press
    • Whiteman J.R. (1975). Some aspects of the mathematics of FE, in the Mathematics of FE and Applications II. MAFELAP 1975. Academic Press.
    • (1975) MAFELAP 1975
    • Whiteman, J.R.1
  • 138
    • 0000561596 scopus 로고
    • On the robustness of ILU smoothing
    • Wittum G. (1989). On the robustness of ILU smoothing. SIAM J. Sci. Stat. Comput., 10, 699-717.
    • (1989) SIAM J. Sci. Stat. Comput. , vol.10 , pp. 699-717
    • Wittum, G.1
  • 139
    • 0001683326 scopus 로고
    • Numerical stability of the Chebyshev method for the solution of large linear systems
    • Wozniakowski H. (1977). Numerical stability of the Chebyshev method for the solution of large linear systems. Num. Math., 28, 191-209.
    • (1977) Num. Math. , vol.28 , pp. 191-209
    • Wozniakowski, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.