Highly Influential

8 Excerpts

- Published 2002

The Chebyshev semiiterative method (CHSIM) is a powerful method for finding the iterative solution of a nonsymmetric real linear system Ax = b if an ellipse excluding the origin well fits the spectrum of A. The asymptotic rate of convergence of the CHSIM for solving the above system under a perturbation of the foci of the optimal ellipse is studied. Several formulae to approximate the asymptotic rates of convergence, up to the first order of a perturbation, are derived. These generalize the results about the sensitivity of the asymptotic rate of convergence to a perturbation of a real-line segment spectrum by Hageman and Young, and by the first author. A numerical example is given to illustrate the theoretical results.

@inproceedings{Li2002ElaTC,
title={Ela the Convergence Rate of the Chebyshev Semiiterative Method under a Perturbation of the Foci of an Elliptic Domain∗},
author={Xiezhang Li and Fangjun Arroyo},
year={2002}
}