Title

The Convergence Rate of the Chebyshev SIM Under a Perturbation of a Complex Line-Segment Spectrum

Document Type

Article

Publication Date

11-15-1995

Publication Title

Linear Algebra and Its Applications

DOI

10.1016/0024-3795(93)00361-3

ISSN

0024-3795

Abstract

The Chebyshev semiiterative method (chsim) is probably the best known and most often used method for the iterative solution of linear system x = Tx + c, where the spectrum of T is located in a complex line segment [α, β] excluding 1. The asymptotic convergence factor (ACF) of the chsim, under a perturbation of [α, β], is considered. Several formulae for the approximation to the ACFs, up to the second order of a perturbation, are derived. This generalizes the results about the sensitivity of the asymptotic rate of convergence to the estimated eigenvalues by Hageman and Young in the case that both α and β are real. Two numerical examples are given to illustrate the theoretical results.

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