Title

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.

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