Differences in the effects of rounding errors in Krylov solvers for symmetric indefinite linear systems

Gerard L.G. Sleijpen*, Henk A. Van Der Vorst, Jan Modersitzki

*Korrespondierende/r Autor/-in für diese Arbeit
36 Zitate (Scopus)

Abstract

The three-term Lanczos process for a symmetric matrix leads to bases for Krylov subspaces of increasing dimension. The Lanczos basis, together with the recurrence coefficients, can be used for the solution of symmetric indefinite linear systems, by solving a reduced system in one way or another. This leads to well-known methods: MINRES (minimal residual), GMRES (generalized minimal residual), and SYMMLQ (symmetric LQ). We will discuss in what way and to what extent these approaches differ in their sensitivity to rounding errors. In our analysis we will assume that the Lanczos basis is generated in exactly the same way for the different methods, and we will not consider the errors in the Lanczos process itself. We will show that the method of solution may lead, under certain circumstances, to large additional errors, which are not corrected by continuing the iteration process. Our findings are supported and illustrated by numerical examples.

OriginalspracheEnglisch
ZeitschriftSIAM Journal on Matrix Analysis and Applications
Jahrgang22
Ausgabenummer3
Seiten (von - bis)726-751
Seitenumfang26
ISSN0895-4798
DOIs
PublikationsstatusVeröffentlicht - 01.01.2000

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