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TitleAutomatic Generation of Numerical Redundancies for Non-Linear Constraint Solving
Author(s) Frederic Benhamou, Laurent Granvilliers
TextF. Benhamou and L. Granvilliers. Automatic Generation of Numerical Redundancies for Non-Linear Constraint Solving. Reliable Computing, 3(3):335-344, 1997.
TypeArticle in Journal
AbstractIn this paper we present a framework for the cooperation of symbolic
and propagation-based numerical solvers over the real numbers. This
cooperation is expressed in terms of fixed points of closure operators over a complete lattice of constraint systems. In a second part we instantiate this framework to a particular cooperation scheme, where propagation is associated to pruning operators implementing interval algorithms enclosing the possible solutions of constraint systems,
whereas symbolic methods are mainly devoted to generate redundant
constraints. When carefully chosen, it is well known that the addition of
redundant constraint drastically improve the performances of systems based on local consistency (e.g. Prolog IV or Newton). We propose here a method which computes sets of redundant polynomials called partial Grobner bases and show on some benchmarks the advantages of such computations.
KeywordsNumerical constraints, interval constraints, approximate solving, local consistency, propagation methods, interval Newton, Gröbner bases
JournalReliable Computing
Pages335 - 344
Translation No
Refereed No