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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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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Abstract 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.
AbstractList 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.
Author Hu, Jingjing
Ma, Changfeng
Ke, Yifen
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