Global solutions of well-constrained transcendental systems using expression trees and a single solution test

Maxim Aizenshtein*, Michael Barton, Gershon Elber

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We present an algorithm which is capable of globally solving a well-constrained transcendental system over some sub-domain , isolating all roots. Such a system consists of n unknowns and n regular functions, where each may contain non-algebraic (transcendental) functions like sin, or log. Every equation is considered as a hyper-surface in and thus a bounding cone of its normal field can be defined over a small enough sub-domain of D. A simple test that checks the mutual configuration of these bounding cones is used that, if satisfied, guarantees at most one zero exists within the given domain. Numerical methods are then used to trace the zero. If the test fails, the domain is subdivided. Every equation is handled as an expression tree, with polynomial functions at the leaves, prescribing the domain. The tree is processed from its leaves, for which simple bounding cones are constructed, to its root, which allows to efficiently build a final bounding cone of the normal field of the whole expression. The algorithm is demonstrated on curve-curve and curve-surface intersection problems.

Original languageEnglish (US)
Title of host publicationAdvances in Geometric Modeling and Processing - 6th International Conference, GMP 2010, Proceedings
Pages1-18
Number of pages18
DOIs
StatePublished - Jul 21 2010
Event6th International Conference on Advances in Geometric Modeling and Processing, GMP 2010 - Castro Urdiales, Spain
Duration: Jun 16 2010Jun 18 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6130 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Advances in Geometric Modeling and Processing, GMP 2010
CountrySpain
CityCastro Urdiales
Period06/16/1006/18/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Global solutions of well-constrained transcendental systems using expression trees and a single solution test'. Together they form a unique fingerprint.

Cite this