CG-type algorithms to solve symmetric matrix equations

The global FOM and GMRES are among the effective algorithms to solve linear system of equations with multiple right-hand sides. In this paper, we study these algorithms in the case that the coefficient matrix is symmetric and extract two CG-type algorithms for solving symmetric linear systems of equations with multiple right-hand sides. Then, we compare the numerical performance of the new algorithms with some available methods. Numerical experiments are done on some test matrices from Harwell–Boeing collection.