Residual Iterative Method for Solving Absolute Value Equations

Abstract

We suggest and analyze a residual iterative method for solving absolute value equations $Ax-\left|x\right|=b$ where $A\in R^{n\times n}$, $b\in R^n$ are given and $x\in R^n$ is unknown, using the projection technique. We also discuss the convergence of the proposed method. Several examples are given to illustrate the implementation and efficiency of the method. Comparison with other methods is also given. Results proved in this paper may stimulate further research in this fascinating field.