Rump, Siegfried M.Siegfried M.RumpGraillat, StefStefGraillat2021-01-212021-01-212009-10-16Numerical Algorithms 3 (54): 359-377 (2010)http://hdl.handle.net/11420/8535It 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 paper we 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 f we 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.en1572-926520093359377Springer Science Business Media B.V.Double rootsError boundsINTLABMultiple rootsNonlinear equationsVerificationInformatikJournal Article10.1007/s11075-009-9339-3Other