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.
Recommended Citation
Li, Xiezhang.
1995.
"The Convergence Rate of the Chebyshev SIM Under a Perturbation of a Complex Line-Segment Spectrum."
Linear Algebra and Its Applications, 230: 47-60.
doi: 10.1016/0024-3795(93)00361-3
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/560
