A verification method for enclosing solutions of absolute value equations
The authors consider the absolue value equations (AVE), \(Ax-|x| =b\), where \(A \in \mathbb{R}^{n \times n}\), and \(b \in \mathbb{R}^{n}\). Determining the existence of a solution is a NP-hard problem. The authors give a sufficient condition to guarantee that a given interval vector contains an exact solution of AVE. Their results are based on the use of interval arithmetic. Given an initial enclosure of a solution, they propose two new interval iterations that converge to that solution under mild assumptions. They also give some methods to compute an initial interval that contains a solution when the matrix \(A\) has some special properties. They also present some numerical experiments that confirm the power of their methods.
scientific article; zbMATH DE number 6148951