NDLI: Krylov sequences of maximal length and convergence of GMRES

Content Provider	Springer Nature Link
Author	Pták, V. Strakoš, Z. Arioli, M.
Copyright Year	1998
Abstract	In most practical cases, the convergence of the GMRES method applied to a linear algebraic systemAx=b is determined by the distribution of eigenvalues ofA. In theory, however, the information about the eigenvalues alone is not sufficient for determining the convergence. In this paper the previous work of Greenbaum et al. is extended in the following direction. It is given a complete parametrization of the set of all pairs {A, b} for which GMRES(A, b) generates the prescribed convergence curve while the matrixA has the prescribed eigenvalues. Moreover, a characterization of the right hand sidesb for which the GMRES(A, b) converges exactly inm steps, wherem is the degree of the minimal polynomial ofA, is given.
Ending Page	643
Page Count	8
Starting Page	636
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	4
Volume Number	38
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1998-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	GMRES method Jordan canonical form Computational Mathematics and Numerical Analysis convergence Iterative methods for linear systems Numeric Computing Krylov sequences Eigenvalues, eigenvectors Mathematics Minimal polynomial
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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Krylov sequences of maximal length and convergence of GMRES