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Volumn 18, Issue 2, 1997, Pages 419-434

A stabilized QMR version of block BICG

Author keywords

Block iterative methods; Krylov subspace; Large linear systems; Multiple right hand sides; Two sided Gram Schmidt

Indexed keywords


EID: 0031493596     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479894264673     Document Type: Article
Times cited : (31)

References (33)
  • 1
    • 0040145887 scopus 로고
    • Techniques for accelerating the block cimmino method
    • J. J. Dongarra, K. Kennedy, P. Messina, D. C. Sorensen, and R. G. Voigt, eds., SIAM, Philadelphia, PA
    • M. ARIOLI, I. DUFF, D. RUIZ, AND M. SADKANE, Techniques for accelerating the block Cimmino method, in Proc. Fifth SIAM Conf. Parallel Processing for Scientific Computing, J. J. Dongarra, K. Kennedy, P. Messina, D. C. Sorensen, and R. G. Voigt, eds., SIAM, Philadelphia, PA, 1992, pp 98-104.
    • (1992) Proc. Fifth SIAM Conf. Parallel Processing for Scientific Computing , pp. 98-104
    • Arioli, M.1    Duff, I.2    Ruiz, D.3    Sadkane, M.4
  • 2
    • 21344492025 scopus 로고
    • An analysis of the composite step biconjugate gradient method
    • R. E. BANK AND T. F. CHAN, An analysis of the composite step biconjugate gradient method, Numer. Math., 66 (1993), pp. 293-319.
    • (1993) Numer. Math. , vol.66 , pp. 293-319
    • Bank, R.E.1    Chan, T.F.2
  • 3
    • 0026104373 scopus 로고
    • The nonsymmetric Lanczos algorithm and controllability
    • D. L. BOLEY AND G. H. GOLUB, The nonsymmetric Lanczos algorithm and controllability, Systems Control Lett., 16 (1991), pp. 97-105.
    • (1991) Systems Control Lett. , vol.16 , pp. 97-105
    • Boley, D.L.1    Golub, G.H.2
  • 4
    • 21144473062 scopus 로고
    • A breakdown-free Lanczos type algorithm for solving linear systems
    • C. BREZINSKI, M. R. ZAGLIA, AND H. SADOK, A breakdown-free Lanczos type algorithm for solving linear systems, Numer. Math., 63 (1992), pp. 29-38.
    • (1992) Numer. Math. , vol.63 , pp. 29-38
    • Brezinski, C.1    Zaglia, M.R.2    Sadok, H.3
  • 5
    • 0040145879 scopus 로고
    • An analog of the Gram-Schmidt algorithm for complex bilinear forms and diagonalization of complex symmetric matrices
    • The Johns Hopkins University, Baltimore, MD
    • D. CHOUDHURY AND R. A. HORN, An Analog of the Gram-Schmidt Algorithm for Complex Bilinear Forms and Diagonalization of Complex Symmetric Matrices, Tech. report 454, The Johns Hopkins University, Baltimore, MD, 1986.
    • (1986) Tech. Report 454
    • Choudhury, D.1    Horn, R.A.2
  • 6
    • 0040654480 scopus 로고
    • Peaks and plateaus in Lanczos methods for solving nonsymmetric systems of equations Ax = b
    • IBM T. J. Watson Research Center
    • J. K. CULLUM, Peaks and Plateaus in Lanczos Methods for Solving Nonsymmetric Systems of Equations Ax = b, Tech. report RC 18084, IBM T. J. Watson Research Center, 1992.
    • (1992) Tech. Report RC 18084
    • Cullum, J.K.1
  • 8
    • 0004109578 scopus 로고
    • User's guide for the Harwell-boeing sparse matrix collection (Release I)
    • CERFACS, Toulouse Cedex, France
    • I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, User's Guide for the Harwell-Boeing Sparse Matrix Collection (Release I), Tech. report TR/PA/92/86, CERFACS, Toulouse Cedex, France, 1992.
    • (1992) Tech. Report TR/PA/92/86
    • Duff, I.S.1    Grimes, R.G.2    Lewis, J.G.3
  • 9
    • 0007702899 scopus 로고
    • Transpose-free quasi-minimal residual methods for non-Hermitian linear systems
    • G. H. Golub, A. Greenbaum, and M. Luskin, eds., Springer-Verlag, New York
    • R. W. FREUND, Transpose-free quasi-minimal residual methods for non-Hermitian linear systems, in Recent Advances in Iterative Methods, IMA Volumes in Mathematics and Its Applications 60, G. H. Golub, A. Greenbaum, and M. Luskin, eds., Springer-Verlag, New York, 1994, pp. 69-94.
    • (1994) Recent Advances in Iterative Methods, IMA Volumes in Mathematics and Its Applications , vol.60 , pp. 69-94
    • Freund, R.W.1
  • 10
    • 0001378925 scopus 로고
    • An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
    • R. W. FREUND, M. H. GUTKNECHT, AND N. M. NACHTIGAL, An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, SIAM J. Sci. Comput., 14 (1993), pp. 137-158.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 137-158
    • Freund, R.W.1    Gutknecht, M.H.2    Nachtigal, N.M.3
  • 11
    • 25444452938 scopus 로고
    • QMR: A quasi-minimal residual method for non-hermitian linear systems
    • R. W. FREUND AND N. M. NACHTIGAL, QMR: A quasi-minimal residual method for non-Hermitian linear systems, Numer. Math., 60 (1991), pp. 315-339.
    • (1991) Numer. Math. , vol.60 , pp. 315-339
    • Freund, R.W.1    Nachtigal, N.M.2
  • 12
    • 0000806356 scopus 로고
    • An implementation of the QMR method based on coupled two-term recurrences
    • R. W. FREUND AND N. M. NACHTIGAL, An implementation of the QMR method based on coupled two-term recurrences, SIAM J. Sci. Comput., 15 (1994), pp. 313-337.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 313-337
    • Freund, R.W.1    Nachtigal, N.M.2
  • 15
    • 0038961504 scopus 로고
    • A completed theory of the unsymmetric Lanczos process and related algorithms. II
    • IPS, ETH-Zentrum
    • M. H. GUTKNECHT, A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. II, Tech. report 90.16, IPS, ETH-Zentrum, 1990.
    • (1990) Tech. Report 90.16
    • Gutknecht, M.H.1
  • 16
    • 0000497979 scopus 로고
    • A completed theory of the unsymmetric Lanczos process and related algorithms. I
    • M. H. GUTKNECHT, A completed theory of the unsymmetric Lanczos process and related algorithms. I, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 594-639.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 594-639
    • Gutknecht, M.H.1
  • 17
    • 0000090638 scopus 로고
    • Lanczos methods for the solution of nonsymmetric systems of linear equations
    • W. D. JOUBERT, Lanczos methods for the solution of nonsymmetric systems of linear equations, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 926-943.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 926-943
    • Joubert, W.D.1
  • 19
    • 0000094594 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • C. LANCZOS, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45 (1950), pp. 255-282.
    • (1950) J. Res. Nat. Bur. Standards , vol.45 , pp. 255-282
    • Lanczos, C.1
  • 20
    • 0004071490 scopus 로고
    • Algorithms for sparse matrix eigenvalue problems
    • Department of Computer Science, Stanford University, Stanford, CA
    • J. LEWIS, Algorithms for sparse matrix eigenvalue problems, Tech. report STAN-CS-77-595, Department of Computer Science, Stanford University, Stanford, CA, 1977.
    • (1977) Tech. Report StAN-CS-77-595
    • Lewis, J.1
  • 21
    • 0003554146 scopus 로고
    • Natick, MA
    • THE MATHWORKS, INC., MATLAB User's Guide, Natick, MA, 1993.
    • (1993) MATLAB User's Guide
  • 22
    • 0343005865 scopus 로고
    • Variable block CG algorithms for solving large sparse symmetric positive definite linear systems on parallel computers, I: General iterative scheme
    • A. A. NIKISHIN AND A. Y. YEREMIN, Variable block CG algorithms for solving large sparse symmetric positive definite linear systems on parallel computers, I: General iterative scheme, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1135-1153.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1135-1153
    • Nikishin, A.A.1    Yeremin, A.Y.2
  • 23
    • 0001084178 scopus 로고
    • The block conjugate gradient algorithm and related methods
    • D. P. O'LEARY, The block conjugate gradient algorithm and related methods, Linear Algebra Appl., 29 (1980), pp. 293-322.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 293-322
    • O'Leary, D.P.1
  • 24
    • 0000131773 scopus 로고
    • Reduction to triangular form and minimal realizations
    • B. N. PARLETT, Reduction to triangular form and minimal realizations, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 567-593.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 567-593
    • Parlett, B.N.1
  • 25
    • 84966231631 scopus 로고
    • A look-ahead Lanczos algorithm for unsymmetric matrices
    • B. N. PARLETT, D. R. TAYLOR, AND Z. A. LIU, A look-ahead Lanczos algorithm for unsymmetric matrices, Math. Comp., 44 (1985), pp. 105-124.
    • (1985) Math. Comp. , vol.44 , pp. 105-124
    • Parlett, B.N.1    Taylor, D.R.2    Liu, Z.A.3
  • 26
    • 84968508607 scopus 로고
    • Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices
    • A. RUHE, Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices, Math. Comp., 33 (1979), pp. 680-687.
    • (1979) Math. Comp. , vol.33 , pp. 680-687
    • Ruhe, A.1
  • 27
    • 0003550735 scopus 로고
    • SPARSKIT: A basic tool kit for sparse matrix computation
    • Center for Supercomputing Research and Development, University of Illinois at Urbana-Champaign
    • Y. SAAD, SPARSKIT: A Basic Tool Kit for Sparse Matrix Computation, Tech. report 1029, Center for Supercomputing Research and Development, University of Illinois at Urbana-Champaign, 1990.
    • (1990) Tech. Report 1029
    • Saad, Y.1
  • 28
    • 0038961572 scopus 로고
    • A new approach to construction of efficient iterative schemes for massively parallel algorithms: Variable block CG and BiCG methods and variable block arnoldi procedure
    • R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed, eds., Philadelphia, PA
    • H. D. SIMON AND A. YEREMIN, A new approach to construction of efficient iterative schemes for massively parallel algorithms: Variable block CG and BiCG methods and variable block Arnoldi procedure, in Proc. Sixth SIAM Conf. Parallel Processing for Scientific Computing, R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed, eds., Philadelphia, PA, 1993, pp. 57-60.
    • (1993) Proc. Sixth SIAM Conf. Parallel Processing for Scientific Computing , pp. 57-60
    • Simon, H.D.1    Yeremin, A.2
  • 29
    • 0038961569 scopus 로고
    • Iterative methods for complex symmetric systems with multiple right-hand sides
    • Center for Supercomputing Research and Development, University of Illinois at Urbana-Champaign
    • V. SIMONCINI AND E. GALLOPOULOS, Iterative Methods for Complex Symmetric Systems with Multiple Right-Hand Sides, Tech. report 1322, Center for Supercomputing Research and Development, University of Illinois at Urbana-Champaign, 1993.
    • (1993) Tech. Report 1322
    • Simoncini, V.1    Gallopoulos, E.2
  • 30
    • 0001448449 scopus 로고
    • An iterative method for nonsymmetric systems with multiple right-hand sides
    • V. SIMONCINI AND E. GALLOPOULOS, An iterative method for nonsymmetric systems with multiple right-hand sides, SIAM J. Sci. Comput., 16 (1995), pp. 917-933.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 917-933
    • Simoncini, V.1    Gallopoulos, E.2
  • 31
    • 0041540457 scopus 로고    scopus 로고
    • Convergence properties of block gmres and matrix polynomials
    • V. SIMONCINI AND E. GALLOPOULOS, Convergence properties of block GMRES and matrix polynomials, Linear Algebra Appl., 247 (1996), pp. 97-119.
    • (1996) Linear Algebra Appl. , vol.247 , pp. 97-119
    • Simoncini, V.1    Gallopoulos, E.2
  • 33
    • 0000848766 scopus 로고
    • Residual smoothing techniques for iterative methods
    • L. ZHOU AND H. F. WALKER, Residual smoothing techniques for iterative methods, SIAM J. Sci. Comput., 15 (1994), pp. 297-312.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 297-312
    • Zhou, L.1    Walker, H.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.