Year: 1998
Author: Zhihao Cao
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 6 : pp. 539–550
Abstract
This paper extends the results by E.M. Kasenally$^{[7]}$ on a Generalized Minimum Backward Error Algorithm for nonsymmetric linear systems $Ax=b$ to the problem in which perturbations are simultaneously permitted on $A$ and $b$. The approach adopted by Kasenally has been to view the approximate solution as the exact solution to a perturbed linear system in which changes are permitted to the matrix $A$ only. The new method introduced in this paper is a Krylov subspace iterative method which minimizes the norm of the perturbations to both the observation vector $b$ and the data matrix $A$ and has better performance than the Kasenally's method and the restarted GMRES ${\rm method}^{[12]}$. The minimization problem amounts to computing the smallest singular value and the corresponding right singular vector of a low-order upper-Hessenberg matrix. Theoretical properties of the algorithm are discussed and practical implementation issues are considered. The numerical examples are also given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9181
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 6 : pp. 539–550
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Nonsymmetric linear systems Iterative methods Backward error.