Verified error bounds for multiple roots of systems of nonlinear equations

Publikationstyp
Journal Article
Date Issued
2009-10-16
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Graillat, Stef  
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/8535
Journal
Numerical Algorithms  
Volume
54
Issue
3
Start Page
359
End Page
377
Citation
Numerical Algorithms 3 (54): 359-377 (2010)
Publisher DOI
10.1007/s11075-009-9339-3
Scopus ID
2-s2.0-77953478326
Publisher
Springer Science Business Media B.V.
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 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.
Subjects
Double roots
Error bounds
INTLAB
Multiple roots
Nonlinear equations
Verification
DDC Class
004: Informatik