A new iterative method to solve the absolute value equation

Document Type : Original Article

Authors
Salman Sheikhi ΒΆ
Hamid Esmaeili
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran.
10.22034/maco.5.2.3
Abstract
This study presents a modified version of the Rohn iterative method to solve the absolute value equation in the form $Ax-|x|-b=0$, where $A$ is a matrix such that the norm of its inverse is less than $1$. 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 $100$ randomly generated absolute value equations of various dimensions. In total, $900$ problems are solved.

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Mathematical Analysis and Convex Optimization
Volume 5, Issue 2
December 2025