Generalized global conjugate gradient squared algorithm

In this paper, a generalized global conjugate gradient squared method for solving nonsymmetric linear systems with multiple right-hand sides is presented. The method can be derived by using products of two nearby global BiCG polynomials and formal orthogonal polynomials, of which global CGS and global BiCGSTAB are just particular cases. We also show to apply the method for solving the Sylvester matrix equation. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.