An algorithm for symmetric indefinite linear systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1270.65020
author: Dandan Chen
author: Liang Li
author: Ting-Zhu Huang
publication date: 2012-10-01T00:00:00Z
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F08
zbMATH DE Number: 6088967
zbMATH Keywords: symmetric indefinite linear system
zbMATH Keywords: weighted matching
zbMATH Keywords: pivoting
zbMATH Keywords: incomplete \({LDL}^{\mathrm T}\) factorization
zbMATH Keywords: boundedly partial pivoting
zbMATH Keywords: preconditioning
zbMATH Keywords: algorithm
zbMATH Keywords: backward stability
zbMATH Keywords: SQMR iterative method
MaRDI profile type: Publication
title: An algorithm for symmetric indefinite linear systems
published in: Journal of Computational Analysis and Applications
review text: The authors consider an algorithm for solving a symmetric indefinite system \(Ax=b\). The preprocessing, based on the weighted matchings, is proposed to the original system to gain a new (symmetric indefinite) linear system \(\hat A \hat x= \hat b\). The main goal of this paper is to present the so-called boundedly partial pivoting in the incomplete \(LDL^{\text{T}}\) factorization of \(\hat A\) with an error \(E\): \(M:=LDL^{\text{T}}=\hat A-E\). It is backward stable due to boundedness of the lower triangular factor \(L\). Moreover, in this pivoting besides concerning the tridiagonal pivoting algorithm there exist no permutations of rows and columns. Lastly, the solution of \(M^{-1}\hat A \hat x=M^{-1} \hat b\) is obtained in terms of the SQMR iterative method.
description: scientific article; zbMATH DE number 6088967