The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix

ABSTRACT

In this paper, an iterative algorithm is presented for solving a class of generalized coupled Sylvester-transpose linear matrix equations over centrosymmetric or anti-centrosymmetric matrix. If the matrix equations are consistent, the solution through the iterative method can be obtained within finite steps without round-off error for any initial centrosymmentirc or anti-centrosymmetric value. Furthermore, one method is provided by choosing the special initial matrices to obtain the least norm solution. Finally, numerical examples are presented to demonstrate the efficiency of the algorithm we have proposed.

KEYWORDS:

• Generalized coupled Sylvester-transpose equations
• modified conjugate gradient method
• centrosymmetric or anti-centrosymmetric matrix
• least norm solution
• numerical experiment

2010 AMS SUBJECT CLASSIFICATION:

• 65F10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by National Science Foundation of China [41725017, 41590864] and National Basic Research Program of China under grant number [2014CB845906]. It is also partially supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences [XDB18010202] and Fujian Natural Science Foundation [2016J01005].