AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES

Changfeng Ma; Tongxin Yan

doi:10.11948/20190184

2020 Volume 10 Issue 4

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Changfeng Ma, Tongxin Yan. AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1282-1310. doi: 10.11948/20190184

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Changfeng Ma, Tongxin Yan. AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1282-1310. doi: 10.11948/20190184

AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES

Changfeng Ma^1,2,
Tongxin Yan^1, ,

1.
College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350117, China
2.
School of Mathematics and Physics, Fujian University of Technology, Fuzhou 350108, China

Corresponding author: Email: macf@fjnu.edu.cn(C. Ma)

Abstract

Abstract

This paper presents an iterative algorithm to solve a class of generalized coupled Sylvester-transpose matrix equations over bisymmetric or skew-anti-symmetric matrices. When the matrix equations are consistent, the bisymmetric or skew-anti-symmetric solutions can be obtained within finite iteration steps in the absence of round-off errors for any initial bisymmetric or skew-anti-symmetric matrices by the proposed iterative algorithm. In addition, we can obtain the least norm solution by choosing the special initial matrices. Finally, numerical examples are given to demonstrate the iterative algorithm is quite efficient. The merit of our method is that it is easy to implement.
- Generalized coupled Sylvester-transpose matrix equations /
- Bisymmetric matrix /
- Skew-anti-symmetric matrix /
- Iterative algorithm
MSC: 65F10, 15A24

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References

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