Rounding error analysis in solving \(M\)-matrix linear systems of block Hessenberg form
type: Item
instance of: scholarly article
title: Rounding error analysis in solving \(M\)-matrix linear systems of block Hessenberg form
zbMATH Open document ID: 1054.65026
published in: Numerical Algorithms
publication date: 2004-08-19T00:00:00Z
review text: The authors analyze the backward error of an algorithm, proposed by them in [SIAM J. Matrix Anal. 24, 852--876 (2003; Zbl 1038.65022)], to solve block lower Hessenberg systems \(Ax=b\). The analysis uses the relation with block LU factorization proving that the proposed algorithm is backward stable for row diagonal dominant matrices and hence for \(M\)-matrices. The obtained solution is the exact solution of a perturbed system where the perturbation in the vector \(b\) is bounded by the product of the infinite norm of the matrix \(A\), the computed solution, the machine precision and a constant depending on the block size and the number of blocks of the Hessenberg matrix \(A\).
reviewed by: R. Bru
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 2093350
zbMATH Keywords: block Hessenberg matrices
zbMATH Keywords: M-matrices
zbMATH Keywords: recursive Gaussian elimination
zbMATH Keywords: sparse matrices
zbMATH Keywords: error analysis
zbMATH Keywords: algorithm
zbMATH Keywords: LU factorization
zbMATH Keywords: diagonal dominant matrices
author: L. Gemignani
author: Grazia Lotti
MaRDI profile type: Publication
full work available at URL: b:numa.0000033130.75020.0e
OpenAlex ID: W1989504137
DOI: 10.1023/B:NUMA.0000033130.75020.0E
description: scientific article; zbMATH DE number 2093350