ON HYBRID ITERATIVE METHODS FOR NONSYMMETRIC SYSTEMS OF LINEAR-EQUATIONS

Hybrid methods for the solution of systems of linear equations consist of a first phase where some information about the associated coeffici ent matrix is acquired, and a second phase in which a polynomial itera tion designed with respect to this information is used. Most of the hy brid algorithms proposed recently for the solution of nonsymmetric sys tems rely on the direct use of eigenvalue estimates constructed by the Arnoldi process in Phase I. We will show the limitations of this appr oach and propose an alternative, also based on the Arnoldi process, wh ich approximates the field of values of the coefficient matrix and of its inverse in the Krylov subspace. We also report on numerical experi ments comparing the resulting new method with other hybrid algorithms.