Comparison between the convergence rates of the Chebyshev method and the related (2,2)-step methods
Xiezhang Li · Numerical Linear Algebra with Applications · 2000
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. Copyright © 2000 John Wiley & Sons, Ltd.