A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides

Linear Algebra and Its Applications

Volumn 254, Issue 1-3, 1997, Pages 119-157

  Freund, Roland W ^a   Malhotra, Manish ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009598276     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00529-0     Document Type: Article

References (30)

1. J. I. Aliaga, D. L. Boley, R. W. Freund, and V. Hernández, A Lanczos-Type Algorithm for Multiple Starting Vectors, Numerical Analysis Manuscript 96-18, Bell Labs., Murray Hill, N.J., Sept. 1996; available on WWW at http://cm.bell-labs.com/cs/doc/96.
2. W. E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math. 9:17-29 (1951).
3. O. Axelsson, A survey of preconditioned iterative methods for linear systems of algebraic equations, BIT 25:166-187 (1985).
4. Å. Björck, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996.
5. W. E. Boyse and A. A. Seidl, A block QMR method for computing multiple simultaneous solutions to complex symmetric systems, SIAM J. Sci. Comput. 17:263-274 (1996).
6. A. Chapman and Y. Saad, Deflated and Augmented Krylov Subspace Techniques, Supercomputer Institute Research Report UMSI 95/181, Univ. of Minnesota, Minneapolis, Sept. 1995.
7. I. S. Duff, A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices, Oxford U.P., Oxford, 1989.
8. S. C. Eisenstat, Efficient implementation of a class of preconditioned conjugate gradient methods, SIAM J. Sci. Statist. Comput. 2:1-4 (1981).
9. P. Feldmann and R. W. Freund, Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm, Numerical Analysis Manuscript 94-11, AT & T Bell Labs., Murray Hill, N.J., Oct. 1994; available on WWW at http:// cm.bell-labs.com/cs/doc/94.
10. R. W. Freund, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Comput. 13:425-448 (1992).
11. R. W. Freund, Block Quasi-minimal Residual Iterations for Non-Hermitian Linear Systems, Talk at the Colorado Conference on Iterative Methods, Breckenridge, Apr. 1994.
12. 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. 14:137-158 (1993).
13. R. W. Freund and M. Malhotra, A Block QMR Algorithm for Non-Hermitian Linear Systems with Multiple Right-Hand Sides, Numerical Analysis Manuscript 95-09, AT & T Bell Labs., Murray Hill, N.J., Nov. 1995; available on WWW at http://cm.bell-labs.com/cs/doc/95.
14. R. W. Freund and N. M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60:315-339 (1991).
15. R. W. Freund and N. M. Nachtigal, An implementation of the QMR method based on coupled two-term recurrences, SIAM J. Sci. Comput. 15:313-337 (1994).
16. R. W. Freund and N. M. Nachtigal, Software for simplified Lanczos and QMR algorithms, Appl. Numer. Math. 19:319-341 (1995).
17. K. Grosh, Design and Analysis of Computational Methods for Structural Acoustics, Ph.D. Thesis, Stanford Univ., 1994.
18. M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards 49:409-436 (1952).
19. J. B. Keller and D. Givoli, Exact non-reflecting boundary conditions, J. Comput. Phys. 82:172-192 (1989).
20. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards 45:255-282 (1950).
21. C. Lanczos, Solution of systems of linear equations by minimized iterations, J. Res. Nat. Bur. Standards 49:33-53 (1952).
22. M. Malhotra, Iterative Solution Methods for Large-Scale Finite-Element Models in Structural Acoustics, Ph.D. Thesis, Dept. of Civil Engineering, Stanford Univ., 1996.
23. M. Malhotra, R. W. Freund, and P. M. Pinsky, Iterative Solution of Multiple Radiation and Scattering Problems in Structural Acoustics Using a Block Quasi-minimal Residual Algorithm, Numerical Analysis Manuscript 96-11, Bell Labs., Murray Hill, N.J., May 1996; available on WWW at http://cm.bell-labs.com/cs/doc/96.
24. M. Malhotra and P. M. Pinsky, A matrix-free interpretation of the nonlocal Dirichlet-to-Neumann radiation boundary condition, Internat. J. Numer. Methods Engrg. 39:3705-3713 (1996).
25. A. A. Nikishin and A. Yu. 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. 16:1135-1153 (1995).
26. D. P. O'Leary, The block conjugate gradient algorithm and related methods, Linear Algebra Appl. 29:293-322 (1980).
27. A. Ruhe, Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices, Math. Comp. 33:680-687 (1979).
28. H. D. Simon and A. Yu. Yeremin, A new approach to construction of efficient iterative schemes for massively parallel applications: Variable block CG and BiCG methods and variable block Arnoldi procedure, in Proceedings of the Sixth SIAM Conference on Parallel Processing/or Scientific Computing (R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed, Eds.), SIAM, Philadelphia, 1993, pp. 57-60.
29. V. Simoncini, A New Version of Block BICG for Multiple Systems, Manuscript, 1994.
30. V. Simoncini and E. Gallopoulos, An iterative method for nonsymmetric systems with multiple right-hand sides, SIAM J. Sci. Comput. 16:917-933 (1995).