An algorithm for solving the absolute value equation

Abstract

Presented is an algorithm which for each A, B ∈ R^n×n and b ∈ Rⁿ in a finite number
of steps either finds a solution of the equation Ax + B|x| = b, or states existence of a singular matrix S satisfying |S − A|≤|B| (and in most cases also constructs such an S).