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
