Alternating direction methods for solving a class of Sylvester-like matrix equations

Abstract

This paper presents two alternating direction methods for the solution and the best approximate solution of a class of Sylvester-like matrix equations and , where A, B, C, D, G and H are given matrices of suitable sizes. Convergence properties of the proposed algorithms are given. Numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and computing time than one recent algorithm on the tested problems.

Keywords:

• Matrix equations
• alternating direction method
• best approximate solution
• convergence analysis
• numerical experiments

AMS Subject Classifications:

• 65F10
• 15A24

Acknowledgements

The authors are most grateful to the anonymous referees for their constructive comments and helpful suggestions, which greatly improved the original paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The project is supported by the National Natural Science Foundation of China [grant number 11071041]; Fujian Natural Science Foundation [grant number 2016J01005], [grant number 2015J01578].