A Novel Iterative Approach for Absolute Value Equations

This paper studies a new iterative method for solving absolute value equations (AVEs). This new method is very efficient when the system matrix A has singular values greater than 1. The proposed method is a three-step method that converges to the solution very quickly. The linear convergence of the new method is proved under the condition that\(\:\:‖{A}^{-1}‖<\frac{1}{4}\). Several numerical experiments show that the proposed method finds the solution in just two iterations with high accuracy of up to\(\:{\:\:10}^{-15}\).