On iterative methods of higher order for systems of linear algebraic equations

Abstract

The paper is concerned with certain $k$-degree iterative methods for the solution of linear algebraic systems. The successive approximation $x_{\nu +1}$ is determined by means of approximations $x_\nu $, $x_{\nu -1}$, $\dots $, $x_{\nu -k+1}$. In this article to each iterative method of the first degree some $k$-degree iterative method is found in order to accelerate the convergence of the intial method.