The Chebyshev solution of the linear matrix equation \(AX+YB=C\)
type: Item
instance of: scholarly article
title: The Chebyshev solution of the linear matrix equation \(AX+YB=C\)
zbMATH Open document ID: 0557.65024
DOI: 10.1007/BF01389497
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Properties of the Chebyshev solutions of the linear matrix equation \(AX+YB=C\) where \(A, B\) and \(C\) are given matrices of dimensions \(m\times r\), \(s\times n\) and \(m\times n\), respectively, where \(r<m\) and \(s<n\), are investigated. Two particular cases are considered separately. In the first case, \(m=r+1\) and \(n=s+1,\) in the second case \(r=s=1\) and \(m, n\) are arbitrary. For these two cases, under the assumption that the matrices \(A\) and \(B\) are full rank, necessary and sufficient conditions characterizing the Chebyshev solution of \(AX+YB=C\) and the formulas for the Chebyshev error are formulated. An algorithm, which may be applied to compute the Chebyshev solution of \(AX+YB=C\) for these particular cases, is proposed. Some numerical examples are also given.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 3888804
zbMATH Keywords: Chebyshev solutions
zbMATH Keywords: linear matrix equation
zbMATH Keywords: Chebyshev error
zbMATH Keywords: algorithm
zbMATH Keywords: numerical examples
author: Krystyna Ziȩtak
MaRDI profile type: Publication
cites work: A computer program for the Chebyshev solution of overdetermined systems of linear equations
cites work: The matrix equation \(AX-YB=C\)
cites work: Q5737099
cites work: Q5653494
cites work: Q3954262
cites work: Approximations in $L^p $ and Chebyshev Approximations
cites work: Q3868257
cites work: Chebyshev and $l^1 $-Solutions of Linear Equations Using Least Squares Solutions
cites work: Optimal cycles in doubly weighted graphs and approximation of bivariate functions by univariate ones
cites work: Failure of the alternating algorithm for best approximation of multivariate functions
cites work: Some best-approximation theorems in tensor-product spaces
cites work: Chebyshev Solution of n+1 Linear Equations in n + 1 n Unknowns
cites work: Best approximation problems in tensor-product spaces
cites work: The Equations AX - YB = C and AX - XB = C in Matrices
cites work: Composants and βN
cites work: Q3885038
cites work: The Properties of the Minimax Solution of a Non-linear Matrix Equation XY = A
full work available at URL: https://doi.org/10.1007/bf01389497
OpenAlex ID: W2312972437
Recommended article: The Chebyshev solution of certain matrix equations
Recommended article: Properties of the strict Chebyshev solutions of the linear matrix equation \(AX+YB=C\)
Recommended article: Q3818439
Recommended article: Solution of the matrix equation \(AX-XB=C\)
Recommended article: Q5483704
Recommended article: The explicit solution of the matrix equation \(AX-XB = C\)
Recommended article: Q5695491
description: scientific article; zbMATH DE number 3888804