Generalized Chebyshev Acceleration

Abstract

We use generalized Chebyshev polynomials, associated with the root system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_2$$\end{document}, to provide a new semi-iterative method for accelerating simple iterative methods for solving linear systems. We apply this semi-iterative method to the Jacobi method, and give an example. We also analyze the efficiency of our method with sparse matrices of large dimension. There are certain restrictions but the resulting acceleration is rather high.