Existence test for solution of nonlinear systems applying affine arithmetic
Given a continuous differentiable function \(f: \mathbb{R}^m\to\mathbb{R}^m\) and an \(m\)-dimensional interval vector \(X\) criteria are derived for verifying the existence of a zero \(x^*\in X\) of \(f\). Moreover, subsets of \(X\) can be given which do not contain a zero of \(f\). The criteria are based on affine arithmetic and Brouwer's fixed point theorem. A new test for existence and uniqueness of a zero of \(f\) is listed, many references for additional tests are given. Two numerical examples compare some of them with the new one showing that the latter succeeds in a shorter time than the other ones.
scientific article; zbMATH DE number 5121424
scientific article