Solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices

Abstract

In many areas of principal component analysis, biology, electricity, solid mechanics, automatics control theory and vibration theory, linear matrix equations can be encountered. The presented paper proposes first an iterative method for finding the generalized bisymmetric solution to the generalized coupled Sylvester matrix equations. Second, when the generalized coupled Sylvester matrix equations matrix are consistent, for any generalized bisymmetric initial iterative matrix pair, we can obtain the generalized bisymmetric solution within finite iterative steps in the absence of round-off errors. Furthermore, the optimal approximate generalized bisymmetric solution of the matrix equation for a given generalized bisymmetric matrix can be obtained by finding the least-norm generalized bisymmetric solution of new generalized coupled Sylvester matrix equations. Finally, numerical examples are presented to support the theoretical results of this paper.