Mathematical Sciences: Faculty Publications
Comparison between the Convergence Rates of the Chebyshev Method and the Related (2,2)-Step Methods
Document Type
Article
Publication Date
5-2000
Publication Title
Journal of Numerical Linear Algebra with Applications
DOI
10.1002/1099-1506(200005)7:4<169::AID-NLA192>3.0.CO;2-V
ISSN
1099-1506
Abstract
An optimal Chebyshev method for solving Ax = b, where all the eigenvalues of the real and non-symmetric matrix A are located in the open right half plane, is dependent on an optimal ellips∂Ω*such that the spectrum of A is contrained in Ω*, the closed interior of the ellipse. The relationship between the convergence rates of the Chebyshev method and the closely related (2,2)-step iterative methods are studied. (2,2)-step iterative methods are faster than an optimal Chebyshev method under certain conditions. A numerical example illustrates such an improvement of a (2,2)-step iterative method.
Recommended Citation
Li, Xiezhang.
2000.
"Comparison between the Convergence Rates of the Chebyshev Method and the Related (2,2)-Step Methods."
Journal of Numerical Linear Algebra with Applications, 7 (4): 169-180.
doi: 10.1002/1099-1506(200005)7:4<169::AID-NLA192>3.0.CO;2-V
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/557
Copyright
This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.
