Title

Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic

Authors

Martine C. Ceberio, University of Texas at El PasoFollow
Laurent Granvilliers, IRIN

Publication Date

2000

Document Type

Article

Comments

Ceberio M., Granvilliers L. (2001) Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic. In: Campbell J.A., Roanes-Lozano E. (eds) Artificial Intelligence and Symbolic Computation. AISC 2000. Lecture Notes in Computer Science, vol 1930. Springer, Berlin, Heidelberg

https://doi.org/10.1007/3-540-44990-6_10

Abstract

A reliable symbolic-numeric algorithm for solving nonlinear systems over the reals is designed. The symbolic step generates a new system, where the formulas are different but the solutions are preserved, through partial factorizations of polynomial expressions and constraint inversion. The numeric step is a branch-and-prune algorithm based on interval constraint propagation to compute a set of outer approximations of the solutions. The processing of the inverted constraints by interval arithmetic provides a fast and efficient method to contract the variables' domains. A set of experiments for comparing several constraint solvers is reported.