Result: Solving nonlinear equations by abstraction, Gaussian elimination, and interval methods

Title:
Solving nonlinear equations by abstraction, Gaussian elimination, and interval methods
Authors:
CEBERIO, Martine, GRANVILLIERS, Laurent
Source:
FroCos 2002 : frontiers of combining systems (Santa Margherita Ligure, 8-10 April 2002)Lecture notes in computer science. :117-131
Publisher Information:
Berlin: Springer, 2002.
Publication Year:
2002
Physical Description:
print, 20 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Théorie programmation, Programming theory, Arithmétique intervalle, Interval arithmetic, Aritmética intervalo, Densification, Densificación, Equation non linéaire, Non linear equation, Ecuación no lineal, Méthode Gauss, Gauss method, Método Gauss, Programmation logique avec contrainte, Constraint logic programming, Programación lógica con restricción, Ramification, Branching, Ramificación, Résolution système équation, Equation system solving, Resolución sistema ecuación, Satisfaction contrainte, Constraint satisfaction, Satisfaccion restricción
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
IRIN - University of Nantes - 2, rue de la Houssinière - B.P. 92208, 44322 Nantes, France
ISSN:
0302-9743
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=14054509
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.14054509
Database:
PASCAL Archive

Further Information

The solving engines of most of constraint programming systems use interval-based consistency techniques to process nonlinear systems over the reals. However, few symbolic-interval cooperative solvers are implemented. The challenge is twofold: control of the amount of symbolic computations, and prediction of the accuracy of interval computations over transformed systems. In this paper, we introduce a new symbolic pre-processing for interval branch-and-prune algorithms based on box consistency. The symbolic algorithm computes a linear relaxation by abstraction of the nonlinear terms. The resulting rectangular linear system is processed by Gaussian elimination. Control strategies of the densification of systems during elimination are devised. Three scalable problems known to be hard for box consistency are efficiently solved.