The Convergence Rate of the Chebyshev SIM under a Perturbation of Foci of an Elliptic Domain
Document Type
Presentation
Presentation Date
3-16-2001
Abstract or Description
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.
Sponsorship/Conference/Institution
Southeastern Atlantic Section Society for Industrial and Applied Mathematics Annual Meeting (SIAM-SEAS)
Location
Conway, SC
Recommended Citation
Li, Xiezhang.
2001.
"The Convergence Rate of the Chebyshev SIM under a Perturbation of Foci of an Elliptic Domain."
Department of Mathematical Sciences Faculty Presentations.
Presentation 288.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/288