A Matrix-Form LSQR Iterative Method for Solving the Second-Order Sylvester Matrix Equation EXF2+AXF+CX+BY=D

Abstract

In this paper, an iterative method is proposed to solve the second-order Sylvester matrix equation EXF^{2}+AXF+CX+BY=D with unknown matrix pair [X, Y], based on a matrix form of LSQR algorithm. By this iterative method, we can obtain the minimum Frobenius norm solution pair or the minimum Frobenius norm least squares solution pair over some constrained matrices, such as symmetric, generalized bisymmetric and (R, S)-symmetric matrices.