Structure preserving subspace methods for the general coupled discrete-time periodic matrix equation and its application in antilinear periodic system

Abstract

In this paper, we establish some efficient iteration methods for solving the general coupled discrete-time periodic matrix equation. More concretely, we propose some structure preserving matrix versions of subspace methods, such as bi-conjugate gradient, bi-conjugate residual, conjugate gradient squared, bi-conjugate gradient stabilized, generalized minimal residual and restarted generalized minimal residual methods. We demonstrate experimentally that the proposed iteration methods are feasible and efficient for the periodic matrix equation.

Keywords:

• Periodic matrix equation
• structure preserving
• bi-conjugate gradient method
• bi-conjugate residual method
• subspace projection method

AMS SUBJECT CLASSIFICATIONS:

• 15A24
• 39B42
• 65F10
• 65F30

Acknowledgments

We would like to thank the editor and anonymous referees for their valuable comments and suggestions which have considerably improved this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is supported by National Natural Science Foundation of China (Grant Nos. 12001211, 12071159, 12171168), Natural Science Foundation of Fujian Province, China (Grant Nos. 2022J01194, 2022J01378) and Key Reform and Education in Fujian Province (Grant No. FBJG20200310).