On the stationary and non stationary extrapolation iterative method

Abstract

In this article theoretical results are presented on the extrapolation of the first order iterative method to estimate the optimal value of the extrapolation parameter with the rate of convergence which is found to be depends inversely on the p-condition number of the error's operator matrix. A further extension is considered to estimate the extrapolation parameters for the nonstationary extrapolation method and the rate of convergence is found to be depend inversely on root p. The stationary and non stationary extrapolation methods are considered to define the relevant extrapolation versions for the Jacobi and SOR methods.