Least-squares Hermitian problem of complex matrix equation ( A X B , C X D ) = ( E , F ) $(AXB,CXD)=(E,F)$

Abstract

Abstract In this paper, we present a direct method to solve the least-squares Hermitian problem of the complex matrix equation ( A X B , C X D ) = ( E , F ) $(AXB,CXD)=(E,F)$ with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, F. This method determines the least-squares Hermitian solution with the minimum norm. It relies on a matrix-vector product and the Moore-Penrose generalized inverse. Numerical experiments are presented which demonstrate the efficiency of the proposed method.

Keywords

• matrix equation
• least-squares solution
• Hermitian matrices
• Moore-Penrose generalized inverse