The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations

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• 作者：Na Huang ; Changfeng Ma ; ^{macf@fjnu.edu.cn" class="auth_mail}
• 关键词：Generalized coupled Sylvester-transpose matrix equations ; Modified conjugate gradient method ; Minimum-norm solution ; Least-squares solution ; Numerical experiment
• 刊名：Computers and Mathematics with Applications
• 出版年：May, 2014
• 年：2014
• 卷：67
• 期：8
• 页码：1545-1558
• 全文大小：400 K

文摘

In this paper, we consider the iteration solutions of generalized coupled Sylvester-transpose matrix equations: , . When the coupled matrix equations are consistent, we propose a modified conjugate gradient method to solve the equations and prove that a solution can be obtained within finite iterative steps in the absence of roundoff-error for any initial value. Furthermore, we show that the minimum-norm solution can be got by choosing a special kind of initial matrices. When the coupled matrix equations are inconsistent, we present another modified conjugate gradient method to find the least-squares solution with the minimum-norm. Finally, some numerical examples are given to show the behavior of the considered algorithms.