@Article{JCM-16-6,
author = {Zhihao, Cao},
title = {Total Generalized Minimum Backward Error Algorithm for Solving Nonsymmetric Linear Systems},
journal = {Journal of Computational Mathematics},
year = {1998},
volume = {16},
number = {6},
pages = {539--550},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7139},
doi = {https://doi.org/1998-JCM-9181},
url = {https://global-sci.com/article/85718/total-generalized-minimum-backward-error-algorithm-for-solving-nonsymmetric-linear-systems}
}