Interval algorithm for absolute value equations (Q657417)

The authors consider the absolute value equation \(f(x):= Ax-|x|- b= 0\), \(A\in\mathbb{R}^{n\times n}\), \(b\in\mathbb{R}^n\). They present a generalized Newton method in order to approximate a zero \(x^*\) of \(f\). To this end they use a particular smoothing function \(f_\mu\) for \(f\). With a second algorithm they construct an enclosure of \(x^*\) using interval arithmetical tools, among them the so-called \(\varepsilon\)-inflation. Numerical experiments illustrate the efficiency of both methods.