Some tests of generalized bisection
ACM Transactions on Mathematical Software (TOMS)
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Numeric-symbolic algorithms for evaluating one-dimensional algebraic sets
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Combining Local Consistency, Symbolic Rewriting and Interval Methods
AISMC-3 Proceedings of the International Conference AISMC-3 on Artificial Intelligence and Symbolic Mathematical Computation
Numerica: a modeling language for global optimization
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
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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.