An Adaptive Chebyshev Iterative Method for Nonsymmetric Linear Systems Based on Modiied Moments

Large, sparse nonsymmetric systems of linear equations with a matrix whose eigenvalues lie in the right half plane may be solved by an iterative method based on Chebyshev polynomials for an interval in the complex plane. Knowledge of the convex hull of the spectrum of the matrix is required in order to choose parameters upon which the iteration depends. Adaptive Chebyshev algorithms , in which these parameters are determined by using eigenvalue estimates computed by the power method or modiications thereof, have been described by Manteuuel 18]. This paper presents an adaptive Chebyshev iterative method, in which eigenvalue estimates are computed from modiied moments determined during the iterations. The computation of eigenvalue estimates from modiied moments requires less computer storage than when eigenvalue estimates are computed by a power method and yields faster convergence for many problems.