Overestimation in linear interval equations
SIAM Journal on Numerical Analysis
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
An interval step control for continuation methods
SIAM Journal on Numerical Analysis
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Algorithm 566: FORTRAN Subroutines for Testing Unconstrained Optimization Software [C5], [E4]
ACM Transactions on Mathematical Software (TOMS)
Reliable two-dimensional graphing methods for mathematical formulae with two free variables
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Parallel Robots
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
A branch and prune algorithm for the approximation of non-linear AE-solution sets
Proceedings of the 2006 ACM symposium on Applied computing
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Including ordinary differential equations based constraints in the standard CP framework
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
ICN-RE: redundancy elimination for information-centric networking
Proceedings of the second edition of the ICN workshop on Information-centric networking
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When numerical CSPs are used to solve systems of n equations with n variables, the preconditioned interval Newton operator plays two key roles: First it allows handling the n equations as a global constraint, hence achieving a powerful contraction. Second it can prove rigorously the existence of solutions. However, none of these advantages can be used for under-constrained systems of equations, which have manifolds of solutions. A new framework is proposed in this paper to extend the advantages of the preconditioned interval Newton to under-constrained systems of equations. This is achieved simply by allowing domains of the NCSP to be parallelepipeds, which generalize the boxes usually used as domains.