An Algorithm for Solving the Absolute Value Equation

Authors: Jiří Rohn
Publication year: 2009
Publication type: Článek v odborném periodiku
Periodical: Electronic Journal of Linear Algebra
Projects: Development of methods for solving large scale nonlinear programming and nonsmooth optimization problems
Verification of Hybrid Systems - Exploiting the Synergy with Underlying Constraint Solving Technology
Bibliographic citation: ROHN, Jiří. An Algorithm for Solving the Absolute Value Equation. Electronic Journal of Linear Algebra. 2009, 18(-), 589-599. ISSN 1537-9582. E-ISSN 1081-3810
Dostupné z: doi:10.13001/1081-3810.1332.
DOI: 10.13001/1081-3810.1332
ID: 329208

Abstract

Presented is an algorithm which for each $A,B\in\Rnn$ and $b\in\Rn$ 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 $|S-A|\leq |B|$ (and in most cases also constructs such an $S$).