Abstract.

A new iterative method is proposed to solve systems of linear algebraic equations, Ax = b. The method is based on the concept of homotopy. Similar works have been done in this direction and some special cases of convergence have been addressed. After reviewing the literature, here we study the method in a more general framework and present more cases of convergence. A comparative study of the method from computational cost viewpoint and speed of convergence shows that the new presented method competes well with classic iterative techniques. Also using a convergence control parameter (CCP) of prof. Shi Jun Liao an stationary modification of the method is presented. This modification of the method clarifies two issues, one that Liao’s CCP may fail to be efficient in a linear equation. Also there are cases where this control parameter can extend the convergence cases of the presented homotopy method.

Keywords:

system of linear equations, homotopy analysis method, iterative methods, convergence control parameter, homotopy perturbation method.