Overestimation in linear interval equations
SIAM Journal on Numerical Analysis
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
Testing Unconstrained Optimization Software
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
On the Approximation of Linear AE-Solution Sets
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Octagonal domains for continuous constraints
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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When numerical CSPs are used to solve systems of nequations with nvariables, the interval Newton operator plays a key role: It acts like a global constraint, hence achieving a powerful contraction, and proves rigorously the existence of solutions. However, both advantages cannot 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 interval Newton to under-constrained systems of equations. This is done simply by permitting domains of CSPs to be parallelepipeds instead of the usual boxes.