An iterative algorithm for the generalized reflexive solution of the matrix equations \(AXB = E, CXD = F\)
type: Item
instance of: scholarly article
title: An iterative algorithm for the generalized reflexive solution of the matrix equations \(AXB = E, CXD = F\)
zbMATH Open document ID: 1251.65046
DOI: 10.1155/2012/492951
author: Feng Yin
author: Guang-Xin Huang
author: De-Qin Chen
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: An iterative algorithm is constructed to solve the linear matrix equation pair \(AXB = E, CXD = F\) over generalized reflexive matrix \(X\). When the matrix equation pair \(AXB = E, CXD = F\) is consistent over generalized reflexive matrix \(X\), for any generalized reflexive initial iterative matrix \(X_1\), the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of \(AXB = E, CXD = F\) for a given generalized reflexive matrix \(X_0\) can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair \(A\tilde{X}B = \tilde{E}, C\tilde{X}D = \tilde{F}\) with \(\tilde{E} = E - AX_0B, \tilde{F} = F - CX_0D\). Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 6106226
zbMATH Keywords: generalized reflexive solution
zbMATH Keywords: iterative algorithm
zbMATH Keywords: finite iterative steps
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/492951
OpenAlex ID: W1558614921
Wikidata QID: Q58905994
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description: scientific article; zbMATH DE number 6106226