Matrix form of the Bi-CGSTAB method for solving the coupled Sylvester matrix equations

Abstract

The bi-conjugate gradient stabilised (Bi-CGSTAB) method is one of the efficient computational tools to solve the non-Hermitian linear systems Ax = b. By employing Kronecker product and vectorisation operator, this study investigates the matrix form of the Bi-CGSTAB method for solving the coupled Sylvester matrix equations ∑ki=1(AiXB i+ CiYDi) = M, k i=1(EiXF i + GiYHi) = N [including (second-order) Sylvester and Lyapunov matrix equations as special cases] encountered in many systems and control applications. Several numerical examples are given to compare the efficiency and performance of the investigated method with some existing algorithms. © The Institution of Engineering and Technology 2013.