#### 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 = *T*x + 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 source: https://www.sciencedirect.com/science/article/pii/0024379593003613?via%3Dihub

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/560