The generalized QMRCGSTAB algorithm for solving Sylvester-transpose matrix equations

In this work we generalize the Quasi-Minimal Residual Variant of the Bi-CGSTAB algorithm (QMRCGSTAB) to obtain a matrix iterative method for solving the Sylvester-transpose matrix equation ∑ i = 1 l ( A i X B i + C i X T D i ) = E . In order to compare the generalized algorithm with some existing methods, we present two numerical examples.