TY - JOUR

T1 - Exclusion regions for systems of equations

AU - Schichl, Hermann

AU - Neumaier, Arnold

N1 - Zeitschrift: SIAM Journal on Numerical Analysis
DOI: 10.1137/S0036142902418898
Coden: SJNAA
Affiliations: Institut furš Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
Adressen: Schichl, H.; Institut furš Mathematik; Universität Wien; Strudlhofgasse 4 A-1090 Wien, Austria; email: [email protected]
Source-File: 506Scopus.csv
Import aus Scopus: 2-s2.0-20144370424
Importdatum: 24.01.2007 11:20:30
22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter)
04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)

PY - 2004

Y1 - 2004

N2 - Branch and bound methods for finding all zeros of a nonlinear system of equations in a box frequently have the difficulty that subboxes containing no solution cannot be easily eliminated if there is a nearby zero outside the box. This has the effect that near each zero many small boxes are created by repeated splitting, whose processing may dominate the total work spent on the global search. This paper discusses the reasons for the occurrence of this so-called cluster effect and how to reduce the cluster effect by defining exclusion regions around each zero found that are guaranteed to contain no other zero and hence can safely be discarded. Such exclusion regions are traditionally constructed using uniqueness tests based on the Krawczyk operator or the Kantorovich theorem. These results are reviewed; moreover, refinements are proved that significantly enlarge the size of the exclusion region. Existence and uniqueness tests are also given. Œ 2004 Society for Industrial and Applied Mathematics.

AB - Branch and bound methods for finding all zeros of a nonlinear system of equations in a box frequently have the difficulty that subboxes containing no solution cannot be easily eliminated if there is a nearby zero outside the box. This has the effect that near each zero many small boxes are created by repeated splitting, whose processing may dominate the total work spent on the global search. This paper discusses the reasons for the occurrence of this so-called cluster effect and how to reduce the cluster effect by defining exclusion regions around each zero found that are guaranteed to contain no other zero and hence can safely be discarded. Such exclusion regions are traditionally constructed using uniqueness tests based on the Krawczyk operator or the Kantorovich theorem. These results are reviewed; moreover, refinements are proved that significantly enlarge the size of the exclusion region. Existence and uniqueness tests are also given. Œ 2004 Society for Industrial and Applied Mathematics.

M3 - Article

VL - 42

SP - 383

EP - 408

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 1

ER -