Finite iterative algorithm for the symmetric periodic least squares solutions of a class of periodic Sylvester matrix equations

被引：0
作者：
Baohua Huang
Changfeng Ma
机构：
[1] Fujian Normal University,College of Mathematics and Informatics & FJKLMAA
来源：
Numerical Algorithms | 2019年 / 81卷
关键词：
Periodic matrix equations; Iterative algorithm; Symmetric ; -periodic solution; Least Frobenius norm; Finite number of iterations; Optimal approximation solution;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The present work proposes a finite iterative algorithm to find the least squares solutions of periodic matrix equations over symmetric ξ-periodic matrices. By this algorithm, for any initial symmetric ξ-periodic matrices, the solution group can be obtained in finite iterative steps in the absence of round-off errors, and the solution group with least Frobenius norm can be obtained by choosing a special kind of initial matrices. Furthermore, in the solution set of the above problem, the unique optimal approximation solution group to a given matrix group in the Frobenius norm can be derived by finding the least Frobenius norm symmetric ξ-periodic solution of a new corresponding minimum Frobenius norm problem. Finally, numerical examples are provided to illustrate the efficiency of the proposed algorithm and testify the conclusions suggested in this paper.
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页码：377 / 406
页数：29
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