Generalized conjugate direction algorithm for solving generalized coupled Sylvester transpose matrix equations over reflexive or anti-reflexive matrices

The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative...

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Bibliographic Details
Published inJournal of the Franklin Institute Vol. 359; no. 13; pp. 6958 - 6985
Main Authors Hu, Jingjing, Ke, Yifen, Ma, Changfeng
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2022
Online AccessGet full text
ISSN0016-0032
1879-2693
DOI10.1016/j.jfranklin.2022.07.005

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Summary:The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative steps in the absence of round-off errors for any initial given reflexive (anti-reflexive) matrix group. Furthermore, we can get the minimum-norm solution group by choosing special kinds of initial matrix group. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2022.07.005