AN ADAPTIVE CHEBYSHEV ITERATIVE METHOD FOR NONSYMMETRIC LINEAR-SYSTEMS BASED ON MODIFIED MOMENTS

Large, sparse nonsymmetric systems of linear equations with a matrix w hose eigenvalues lie in the right half plane may be solved by an itera tive method based on Chebyshev polynomials for an interval in the comp lex plane. Knowledge of the convex hull of the spectrum of the matrix is required in order to choose parameters upon which the iteration dep ends. Adaptive Chebyshev algorithms, in which these parameters are det ermined by using eigenvalue estimates computed by the power method or modifications thereof, have been described by Manteuffel [18]. This pa per presents an adaptive Chebyshev iterative method, in which eigenval ue estimates are computed from modified moments determined during the iterations. The computation of eigenvalue estimates from modified mome nts requires less computer storage than when eigenvalue estimates are computed by a power method and yields faster convergence for many prob lems.