Orthogonal polynomials and semi-iterative methods for the Drazin-inverse solution of singular linear systems
type: Item
instance of: scholarly article
title: Orthogonal polynomials and semi-iterative methods for the Drazin-inverse solution of singular linear systems
zbMATH Open document ID: 1019.65026
author: Avram Sidi
author: Y. Kanevsky
published in: Numerische Mathematik
publication date: 2003-03-18T00:00:00Z
review text: The authors present a novel class of semi-iterative methods for the Drazin-inverse solution of consistent and inconsistent singular linear systems. The coefficient matrices of the studied systems of equations are allowed to have arbitrary index and arbitrary spectra in the complex plane. Short review of semi-iterative methods for the Drazin-inverse solution of singular linear systems is presented. The methods and algorithms, which are reported, are based on orthogonal polynomials and can be implemented by four-term recursion relations independently of the index. All the computational details of the algorithms and a complete convergence analysis for the methods are given. The use of the new algorithms and the convergence theory developed is illustrated with a simple numerical example.
reviewed by: Krassimir Georgiev
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A06
zbMATH DE Number: 1884036
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: semi-iterative methods
zbMATH Keywords: Drazin-inverse solution
zbMATH Keywords: singular linear systems
zbMATH Keywords: algorithms
zbMATH Keywords: four-term recursion relations
zbMATH Keywords: convergence
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: s002110100379
OpenAlex ID: W1996363027
DOI: 10.1007/S002110100379
description: scientific article; zbMATH DE number 1884036