A new iterative method to solve the absolute value equation

This study presents a modified version of the Rohn iterative method to solve the absolute value equation in the form Ax-|x|-b=۰, where A is a matrix such that the norm of its inverse is less than ۱. The proposed method converges linearly to the unique solution of the absolute value equation. It offers a low computational cost algorithm that provides an approximate solution with acceptable accuracy after only a few iterations. Furthermore, this study compares the structure and convergence rates of the proposed method, the generalized Newton method, and the standard Rohn method. The potential applications of the proposed method are demonstrated through a comparison with the generalized Newton and Rohn methods, using ۱۰۰ randomly generated absolute value equations of various dimensions. In total, ۹۰۰ problems are solved.

کلیدواژه ها:

Absolute value equation ، A modified Rohn iterative method ، The generalized Newton method