Extending the GPBiCG algorithm for solving the generalized Sylvester-transpose matrix equation

Abstract

By applying Kronecker product and vectorization operator, we extend the generalized product bi-conjugate gradient (GPBiCG) algorithm for solving the generalized Sylvester-transpose matrix equation $\sum\nolimits_{i = 1}^r {(A_i XB_i + C_i X^T D_i ) = E} $ . By using numerical results, we compare the new method with other popular iterative solvers in use today.