Restarted GMRES augmented with eigenvectors for shifted linear systems

International Journal of Computer Mathematics

Volumn 80, Issue 8, 2003, Pages 1037-1047

  Gu, Guiding ^a   Zhang, Jianjun ^a   Li, Zhanwen ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Augmented GMRES method; Restarting; Shifted systems

Indexed keywords

ITERATIVE METHODS; MATHEMATICAL OPERATORS; VECTORS; VIRTUAL REALITY;

AUGMENTED GMRES METHOD; RESTARTING; SHIFTED SYSTEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 28344437296     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/0020716031000103330     Document Type: Article

References (18)

1. Chapman, A. and Saad, Y. (1997). Deflated and augment Krylov subspace techniques. Numerical Linear Algebra with Application, 41, 43-66.
2. Datta, B. and Saad, Y. (1991). Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment. Linear Algebra Appl., 154-156, 225-244.
3. Erhel, J., Burrage, K. and Pohl, B. (1996). Restarted GMRES preconditioned by deflation. J. Comput. Appl. Math., 69, 303-318.
4. Freund, R. W. (1993). Solution of shifted linear systems by quasi-minimal residual iterations. In: Reichel, L., Ruttan, Aa. and Varga, R. S. (Eds.), Numerical Linear Algebra, de Gruyter, Berlin, pp. 101-121.
5. Frommer, A. and Glassner, U. (1998). Restarted GMRES for shifted linear systems. SIAM J. Sci. Comput., 19, 15-26.
6. Frommer, A., Nockel, B., Gusken, S., Lippert, T. and Schilling, K. (1995). Many masses on one stroke: Economic computation of quark propagators. Internat. J. Modern Phys. C, 6, 627-638.
7. Guiding Gu (2002). A seed method for solving nonsymmetric linear systems with multiple right-hand sides. Intern. J. Computer Math., 79, 307-326.
8. Guiding Gu and Zhihao Cao (2001). A block GMRES method augmented with eigenvectors. Appl. Math. Comput., 121, 271-289.
9. Guiding Gu and Hebin Wu (1999). A block EN algorithm for nonsymmnetric linear systems with multiple right-hand sides. Linear Algebra Appl., 299, 1-20.
10. Le Calvez, C. and Molina, B. (1999). Implicitly restarted and deflated GMRES. Numerical Algorithms, 21, 261-285.
11. Morgan, R. B. (1995). A restarted GMRES method augmented with eigenvectors. SIAM J. Matrix Anal. Appl., 16, 1154-1171.
12. Morgan, R. B. (2000). Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations. SIAM J. Matrix Anal. Appl., 21, 1112-1135.
13. Saad, Y. (1996). Iterative Methods for Sparse Linear Systems. PWS Publishing Co., Boston.
14. Saad, Y. (1997). Analysis of augmented Krylov subspace methods. SIAM J. Matrix Anal. Appl., 18, 435-449.
15. Simoncini, V. (2000). On the convergence of restarted Krylov subspace methods. SIAM. J. Matrix Anal. Appl., 22, 430-452.
16. Simoncini, V. and Gallopoulos, E. (1996). A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides. J. Comput. Appl. Math., 66, 457-469.
17. Sweet, R. (1988). A parallel and vector variant of the cyclic reduction algorithm. SIAM J. Sci. Statist. Comput., 9, 89-105.
18. Young, D. and Vona, B. (1992). On the use of rational iterative methods for solving large sparse linear systems. Appl. Numer. Math., 10, 261-278.