On an accelerated procedure of extrapolation

A Yeyios

doi:10.1155/s0161171281000586

Abstract

This paper presents some theoretical results concerning an extrapolation method, based on a completely consistent linear stationary iterative method of first degree, for the numerical solution of the linear system Au = b.The main purpose of the paper is to find ranges for the extrapolation parameter, such that the extrapolation method converges independently of whether the original iterative method is convergent or not.

Highlights

(I.i) where A is a given nonsingular real nn matrix, b is a given real vector and u is the solution-vector, which is to be determined, various iterative methods can be applied
In order to accelerate the rates of convergence of methods like (1.2), various procedures and modifications are used
We study extrapolation method (1.6) in order to find ranges for m in which convergence is achieved in the general case

Summary

Introduction

(I.i) where A is a given nonsingular real nn matrix, b is a given real vector and u is the solution-vector, which is to be determined, various iterative methods can be applied. We consider a completely consistent linear stationary iterative method of first degree Where G is some real matrix, which is called the iteration matrix of the method (1.2), k is some real vector and (). One of them is the extrapolation method based on (1.2). That the idea of using an extrapolation parameter, 0, appeared long ago in the stationary Richardson method [2], based on (i.i), defined by. The problem which arises is how the parameter must be chosen in order to have p(G )< p(G) with @(G )

Objectives

Conclusion