Iterative method for mirror-symmetric solution of matrix equation \(AXB+CYD=E\)
type: Item
instance of: scholarly article
title: Iterative method for mirror-symmetric solution of matrix equation \(AXB+CYD=E\)
zbMATH Open document ID: 1242.65079
author: Jianyong Qiao
author: Sumit K. Garg
published in: Bulletin of the Iranian Mathematical Society
publication date: 2011-07-27T00:00:00Z
review text: An iterative algorithm for the mirror-symmetric solution of the matrix equation \(AXB+CYD=E\) is proposed. It is an extension of the classical conjugate gradient method. Using this algorithm, the solvability of the matrix equation can be determined automatically. If the matrix equation is consistent, it is shown that for a special initial iteration the least norm mirror-symmetric solution can be computed by finite iterations in the absence of round-off errors. Numerical experiments illustrate the efficiency of the algorithm. The paper deals with a special problem of the linear algebra, however, the authors claim that it has important applications, e.g., in pattern recognition, antenna theory, quantum physic, etc.. The mirror-symmetric matrices are defined as the generalization of the centrosymmetric matrices. After proposing the variant of the conjugate gradient method, its properties in a numerous of technical lemmas and theorems are studied. This extends results known from the standard conjugate gradient method. The least norm solution is studied using the Kronecker product. The method is tested on one academic example in the Matlab environment. The precision of computed results is comparable with the computer epsilon.
reviewed by: Radek Kucera
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 5932929
zbMATH Keywords: mirror-symmetric matrices
zbMATH Keywords: matrix equation
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: mirror-symmetric solution
zbMATH Keywords: algorithm
zbMATH Keywords: least norm solution
zbMATH Keywords: numerical experiments
describes a project that uses: Matlab
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5932929