Matrix form of the Bi‐CGSTAB method for solving the coupled Sylvester matrix equations
Masoud Hajarian · IET Control Theory and Applications · 2013
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 ∑ i =1 k ( A i XB i + C i YD i ) = M , ∑ i =1 k ( E i XF i + G i YH i ) = 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.