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A Symbolic-Numerical Branch and Prune Algorithm for Solving Non-linear Polynomial Systems (1998)
| Content Provider | CiteSeerX |
|---|---|
| Author | Granvilliers, Laurent |
| Abstract | : This paper discusses the processing of non-linear polynomial systems using a branch and prune algorithm within the framework of constraint programming. We propose a formalism for a kind of branch and prune algorithm implementing symbolic and numerical methods to reduce the systems with respect to a relation defined from both inclusion of variable domains and inclusion of sets of constraints. The second part of the paper presents an instantiation of this general scheme. The pruning step is implemented as a cooperation of factorizations, substitutions and partial computations of Grobner bases to simplify the systems, and interval Newton methods address the numerical, approximate solving. The branching step creates a partition of domains or generates disjunctive constraints from equations in factorized form. Experimental results from a prototype show that interval methods generally benefit from the symbolic processing of the initial constraints. Key Words: Branch and prune algorithm, n... |
| File Format | |
| Volume Number | 4 |
| Journal | Journal of Universal Computer Science |
| Language | English |
| Publisher Date | 1998-01-01 |
| Access Restriction | Open |
| Subject Keyword | Prune Algorithm Non-linear Polynomial System Symbolic-numerical Branch Second Part Branching Step Partial Computation Interval Method Grobner Base Variable Domain Factorized Form General Scheme Prototype Show Interval Newton Method Generates Disjunctive Constraint Numerical Method Constraint Programming Approximate Solving Key Word Pruning Step Experimental Result Initial Constraint Symbolic Processing |
| Content Type | Text |
| Resource Type | Article |
