Generalized conjugate gradient squared (Q1919946)

A generalized conjugate gradient squared method for solving nonsymmetric linear systems of equations is proposed. Instead of squaring the Bi-CG polynomial as in the conjugate gradient squared (CGS) method, the authors use a product of two nearby Bi-CG polynomials. Therefore, the CGS method is a special case of the proposed generalized CGS method. Numerical examples show that the present approach leads to algorithms with better convergence properties. Furthermore, it is shown that the application of the generalized CGS method as inner iteration method within a Newton's scheme may decrease the number of Newton steps significantly.