Krylov sequences of maximal length and convergence of GMRES

BIT Numerical Mathematics

Volumn 38, Issue 4, 1998, Pages 636-643

  Arioli, M ^a   Ptak V ^b   Strakos Z ^b  

^a CNR   (Italy)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

Author keywords

Convergence; GMRES method; Jordan canonical form; Krylov sequences; Minimal polynomial

Indexed keywords

EID: 0000734143     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510405     Document Type: Article

References (6)

1. A. Greenbaum and Z. Strakoš. Matrices that generate the same Krylov residual spaces, in Recent Advances in Iterative Methods, G. H. Golub, A. Greenbaum, and M. Luskin, eds., Springer-Verlag, Berlin, 1994, pp. 95-118.
2. A. Greenbaum, V. Pták and Z. Strakoš, Any nonincreasing convergence curve is possible for GMRES, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 465-469.
3. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1991.
4. Y. Saad and M. Schultz, A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comp., 7 (1986), pp. 856-869.
5. S. L. Campbell, I. C. F. Ipsen, C. T. Keley, and C. D. Meyer, GMRES and the minimal polynomial, BIT, 36 (1996), pp. 664-675.
6. F. R. Gantmakher, Teorija Matric, Nauka, Moscow, 1988 (in Russian).