A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides

Journal of Computational and Applied Mathematics

Volumn 66, Issue 1-2, 1996, Pages 457-469

  Simoncini, V ^a   Gallopoulos, E ^b,c  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF PATRAS   (Greece)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Block iterative methods; Krylov subspace; Linear systems; Matrix polynomials; Multiple right hand sides

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; MATRIX ALGEBRA; POLYNOMIALS;

BLOCK ITERATIVE METHODS; KRYLOV SUBSPACE; MATRIX POLYNOMIALS; MULTIPLE RIGHT HAND SIDES; NONSYMMETRIC SYSTEMS;

PROBLEM SOLVING;

EID: 0029697287     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(95)00198-0     Document Type: Article

References (19)

1. D. Calvetti and L. Reichel, Application of a block modified Chebyshev algorithm to the iterative solution of symmetric linear systems with multiple right-hand side vectors, Numer. Math. 68 (1994) 3-16.
2. B.N. Datta and Y. Saad, Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment, Linear Algebra Appl. 154-156 (1991) 225-244.
3. I.S. Duff, R.G. Grimes and J.G. Lewis, Sparse matrix test problems, ACM Trans. Math. Software 15 (1989) 1-14.
4. R.W. Freund, Quasi-kernel polynomials and their use in non-Hermitian matrix iterations, J. Comput. Appl. Math. 43 (1992) 135-158.
5. R.W. Freund, Solution of shifted linear systems by quasi-minimal residual iterations, in: L. Reichel, A. Ruttan and R. Varga, Eds., Numerical Linear Algebra (W. de Gruyter, Berlin, 1993) 101-121.
6. R.W. Freund, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comput. 14 (1993) 470-482.
7. E. Gallopoulos and V. Simoncini, Iterative solution of multiple linear systems: Theory, practice, parallelism, and applications, in: B.H.V. Topping and M. Papadrakakis, Eds., Advances in Parallel and Vector Processing for Structural Mechanics: Proc. 2nd International Conf. Computational Structures Technology (Civil-Comp Press, Edinburgh, 1994) 47-51.
8. I. Gohberg, L. Rodman and P. Lancaster, Matrix Polynomials (Academic Press, New York, 1982).
9. G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities (Cambridge University Press, Cambridge, 2nd ed., 1952).
10. W.D. Joubert, A robust GMRES-based adaptive polynomial preconditioning algorithm for nonsymmetric linear systems, SIAM J. Sci. Comput., to appear.
11. M.D. Kent. Chebyshev, Krylov, Lanczos: Matrix relationship and computations, Ph.D. Thesis, Stanford University, 1989.
12. N.M. Nachtigal, L. Reichel and L.N. Trefethen, A hybrid GMRES algorithm for nonsymmetric matrix iterations, SIAM J. Matrix Anal. Appl. 13 (July 1992) 796-825.
13. D.P. O'Leary, The block conjugate gradient algorithm and related methods, Linear Algebra Appl. 29 (1980) 293-322.
14. G. Opfer and G. Schober, Richardson's iteration for nonsymmetric matrices, Linear Algebra Appl. 58 (1984) 343-361.
15. Y. Saad and M.H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Comput. 7(3) (1986) 856-869.
16. P.E. Saylor and D.C. Smolarski, Implementation of an adaptive algorithm for Richardson's method, Linear Algebra Appl. 154-156 (1991) 615-646.
17. V. Simoncini and E. Gallopoulos, Convergence properties of block GMRES and matrix polynomials, Linear Algebra Appl., to appear. Also Tech. Report 1316 (1994 revision), Center for Supercomputing Research and Development.
18. V. Simoncini and E. Gallopoulos, An iterative method for nonsymmetric systems with multiple right-hand sides, SIAM J. Sci. Comput. 16(4) (1995) 917-933.
19. B. Vital, Etude de quelques méthodes de résolution de problèmes linéaires de grande taille sur multiprocesseur, Ph.D. Thesis, Université de Rennes I, Rennes, 1990.