Title: Verified error bounds for multiple roots of systems of nonlinear equations

Abstract:
It is well known that it is an ill-posed problem to decide whether a function has a
multiple root. Even for a univariate polynomial an arbitrary small perturbation of a 
polynomial coefficient may change the answer from yes to no. Let a system of nonlinear 
equations be given. In this talk, we will describe an algorithm for computing verified and 
narrow error bounds with the property that a slightly perturbed system is proved to have
a double root within the computed bounds. For a univariate nonlinear function, we will give
a similar method also for a multiple root. A narrow error bound for the perturbation is 
computed as well. Computational results for systems with up to 1000 unknowns demonstrate
the performance of the methods. This is a joint work with Prof. Siegfried M. Rump.