Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems

Tisseur, Françoise Tisseur (2001) Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications, 22 (4). pp. 1038-1057. ISSN 1095-7162

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Abstract

We examine the behavior of Newton's method in floating point arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable solution of the linear systems. We bound the limiting accuracy and the smallest norm of the residual. The application that motivates this work is iterative refinement for the generalized eigenvalue problem. We show that iterative refinement by Newton's method can be used to improve the forward and backward errors of computed eigenpairs.

Item Type:	Article
Uncontrolled Keywords:	Newton's method; generalized eigenvalue problem; iterative refinement; Cholesky method; backward error; forward error; rounding error analysis; limiting accuracy; limiting residual
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	05 Dec 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/979

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