Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
The Mathematica book (4th edition)
The Mathematica book (4th edition)
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Extending Consistent Domains of Numeric CSP
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Numerica: a modeling language for global optimization
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Box consistency through adaptive shaving
Proceedings of the 2010 ACM Symposium on Applied Computing
Making adaptive an interval constraint propagation algorithm exploiting monotonicity
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Technical Communique: Interval constraint propagation with application to bounded-error estimation
Automatica (Journal of IFAC)
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Interval-based methods can approximate all the real solutions of a system of equations and inequalities. The Box interval constraint propagation algorithm enforces Box consistency. Itsmain procedure BoxNarrow handles one function f corresponding to the revised constraint, and one variable x, replacing the other variables of f by their current intervals. This paper proposes an improved BoxNarrow procedure for narrowing the domain of x when f respects certain conditions. In particular, these conditions are fulfilled when f is polynomial. f is first symbolically rewritten into a new form g. A narrowing step is then run on the non-interval extremal functions that enclose the interval function g. The corresponding algorithm is described and validated on several numerical constraint systems.