Using successive approximations for improving the convergence of GMRES method
A possibility how to improve the convergence of the GMRES method for the iterative solution of the system \((I-T)x=b\) of linear algebraic equations with a nonsymmetric matrix is suggested. It consists in performing \(m\) pre-iterations of the form \(y_{l+1}=Ty_l+b\) before starting GMRES and in putting \(y_m\) as the initial approximation for GMRES. From the practical point of view, such pre-processing seems to be advantageous since one iteration of the pre-processing process costs less work that one of GMRES. Numerical tests confirm this hypothesis and the theory presented in the paper explains this observations.
scientific article; zbMATH DE number 1450157
scientific article