On the Error Computation for Polynomial Based Iteration Methods

Bernd Fischer, Gene H. Golub

Abstract

In this note we investigate the Chebyshev iteration and the conjugate gradient method applied to the system of linear equations Ax = f where A is a symmetric, positive definite matrix. For both methods we present algorithms which approximate during the iteration process the kth error $k= ||x − xk||A. The algorithms are based on the theory of modified moments and Gaussian quadrature. The proposed schemes are also applicable for other polynomial iteration schemes. Several examples, illustrating the performance of the described methods, are presented.
OriginalspracheEnglisch
TitelRecent Advances in Iterative Methods
Redakteure/-innenGene Golub, Mitchell Luskin, Anne Greenbaum
Seitenumfang9
Band60
ErscheinungsortNew York, NY
Herausgeber (Verlag)Springer New York LLC
Erscheinungsdatum1994
Seiten59-67
ISBN (Print)978-1-4613-9355-9
ISBN (elektronisch)978-1-4613-9353-5
DOIs
PublikationsstatusVeröffentlicht - 1994

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