On the generalized ADI method for the matrix equation \(X- AXB\)=\(C\)
type: Item
instance of: scholarly article
title: On the generalized ADI method for the matrix equation \(X- AXB\)=\(C\)
zbMATH Open document ID: 1032.65041
DOI: 10.1016/S0377-0427(02)00917-2
author: J. P. Thiran
author: M. Matelart
author: B. Le Bailly
published in: Journal of Computational and Applied Mathematics
publication date: 2003-08-07T00:00:00Z
review text: The authors consider the generalized alternating direction implicit (ADI) iterative method for solving the matrix equation \(X-AXB=C\). For analysing the convergence of the iterative method a corresponding rational approximation problem is formulated and investigated. A theory on the characterization and uniqueness of the optimal solution is presented. A Remes like algorithm for the computation of that solution is described and its convergence is proved. Finally, numerical experiments are reported.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1961622
zbMATH Keywords: ADI method
zbMATH Keywords: rational approximation
zbMATH Keywords: Remes algorithm
zbMATH Keywords: alternating direction implicit iterative method
zbMATH Keywords: matrix equation
zbMATH Keywords: convergence
zbMATH Keywords: optimal solution
zbMATH Keywords: numerical experiments
reviewed by: Michael Jung
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00917-2
OpenAlex ID: W1984564131
description: scientific article; zbMATH DE number 1961622