Bounding perturbations in zeros of nonlinear systems (Q1611213)

The work is devoted to determines computationally rigorous bounds on solutions \(x\in \mathbb{R}^n\) of nonlinear equations \(F(x,t) =0\in \mathbb{R}^m\), \(m\leq n\), due to small perturbations in the parameter \(t\in \mathbb{R}^l\). Conditions for existence and uniqueness of solutions are given. The obtained algorithms are illustrated by several numerical examples.