You are here: MIMS > EPrints
MIMS EPrints

2007.223: Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems

2007.223: Françoise Tisseur 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

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
209 Kb

DOI: 10.1137/S0895479899359837

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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2007.223
Deposited By:Ms Helen Kirkbright
Deposited On:05 December 2007

Download Statistics: last 4 weeks
Repository Staff Only: edit this item