The Convergence Rate of the Chebyshev SIM under a Perturbation of Foci of an Elliptic Domain
Electronic Journal of Linear Algebra
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.
Li, Xiezhang, Fangjun Arroyo.
"The Convergence Rate of the Chebyshev SIM under a Perturbation of Foci of an Elliptic Domain."
Electronic Journal of Linear Algebra, 9: 55-66.
doi: 10.13001/1081-3810.1073 source: https://www.researchgate.net/publication/228890966_The_convergence_rate_of_the_Chebyshev_semiiterative_method_under_a_perturbation_of_the_foci_of_an_elliptic_domain