New test algorithms for system of absolute value equations
Yiwei Wang, Chu xue, Haijun Wang · Engineering Computations · 2025
Purpose This study presents an interval test numerical iteration method specifically designed to solve a system of absolute value equations (SAVE). The proposed method is valuable and efficient in solving a system of absolute value equations. Several numerical examples are used to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach We investigated the NP-hard system of absolute value equations (SAVE). A new algorithm is designed to compute the unknown solution of SAVE on a digital computer. The new test algorithm procedure consists of two parts. In the first part, a multidimensional interval centered on an approximate solution of the problem is guaranteed to contain an exact solution. In the second part, the new iterative process is guaranteed to converge to the exact solution of SAVE for all initial points in a given multidimensional interval. Numerical results illustrate that the new algorithm is effective and reliable. Findings This study provides empirical insights into how to solve a system of absolute value equations. Originality/value This paper fulfills an identified need to study absolute value equations.