Title

The Superiority of a New Type of (2,2)-Step Iterative Methods Over the Related Chebyshev Method

Document Type

Article

Publication Date

3-15-2005

Publication Title

Applied Mathematics and Computation

DOI

10.1016/j.amc.2003.12.112

ISSN

0096-3003

Abstract

A new type (2,2)-step iterative method related to an optimal Chebyshev method is developed for solving real and nonsymmetric linear systems of the form Ax=b. It is an extension of the (2,2)-step iterative method introduced in [Numer. Linear Algebra Appl. 7 (2000) 169]. The superiority of the new type (2,2)-step iterative method over the optimal Chebyshev method is derived in the case where the known (2,2)-step iterative method may not improve the asymptotic rate of convergence. Two numerical examples are given to illustrate the results.

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