On the Error Computation for Polynomial Based Iteration Methods

Bernd Fischer, Gene H. Golub


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.
Original languageEnglish
Title of host publicationRecent Advances in Iterative Methods
EditorsGene Golub, Mitchell Luskin, Anne Greenbaum
Number of pages9
Place of PublicationNew York, NY
PublisherSpringer New York LLC
Publication date1994
ISBN (Print)978-1-4613-9355-9
ISBN (Electronic)978-1-4613-9353-5
Publication statusPublished - 1994


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