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1 COPRIN - Constraints solving, optimization and robust interval analysis CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech 2 LIGM - Laboratoire d-Informatique Gaspard-Monge 3 LINA - Laboratoire d-Informatique de Nantes Atlantique

Abstract : Inter-block backtracking IBB computes all the solutions of sparse systems of nonlinear equations over the reals. This algorithm, introduced by Bliek et al. 1998 handles a system of equations previously decomposed into a set of small k × k sub-systems, called blocks. Partial solutions are computed in the different blocks in a certain order and combined together to obtain the set of global solutions. When solutions inside blocks are computed with interval-based techniques, IBB can be viewed as a new interval-based algorithm for solving decomposed systems of non-linear equations. Previous implementations used Ilog Solver and its IlcInterval library as a black box, which implied several strong limitations. New versions come from the integration of IBB with the interval-based library Ibex. IBB is now reliable no solution is lost while still gaining at least one order of magnitude w.r.t. solving the entire system. On a sample of benchmarks, we have compared several variants of IBB that differ in the way the contraction-filtering is performed inside blocks and is shared between blocks. We have observed that the use of interval Newton inside blocks has the most positive impact on the robustness and performance of IBB. This modifies the influence of other features, such as intelligent backtracking. Also, an incremental variant of inter-block filtering makes this feature more often fruitful.

Keywords : Intervals Arithmetic Decomposition Solving sparse systems

Autor: Bertrand Neveu - Gilles Trombettoni - Gilles Chabert -



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