The iterative solution of the matrix equation \(XA+BX+C=0\)
type: Item
instance of: scholarly article
title: The iterative solution of the matrix equation \(XA+BX+C=0\)
zbMATH Open document ID: 0663.65032
DOI: 10.1016/0024-3795(88)90008-0
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The paper deals with the linear matrix equation \(XA+BX+C=0\) in the unknown matrix X. The aim is to present a unified theory for the iterative solution of this equation. Two well known iterative algorithms, converging when A and B are stable, are realized as special cases of the proposed unified method. The convergence of the unified algorithm does not depend on the stability of A and B, but occurs whenever the matrix equation has a unique solution. Finally, a theoretical algorithm based on a matrix polynomial is presented; it requires the construction of characteristic or interpolating polynomials.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 4084852
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: linear matrix equation
zbMATH Keywords: iterative algorithms
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: matrix polynomial
author: David F. Miller
reviewed by: Franco Flandoli
describes a project that uses: Algorithm 432
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90008-0
OpenAlex ID: W2004054427
cites work: Matrix Equation $XA + BX = C$
cites work: Numerical solution of \(A^ tS + SA + Q = 0\).
cites work: The numerical solution of&lt;tex&gt;A'Q+QA = -C&lt;/tex&gt;
cites work: Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
cites work: A Hessenberg-Schur method for the problem AX + XB= C
cites work: Explicit Solutions of Linear Matrix Equations
description: scientific article; zbMATH DE number 4084852