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OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS

2010

The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…

[ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA]Linear programmingPolytopeBernstein polynomials01 natural sciencesSimplex algorithmApplied mathematicssimplex algorithm0101 mathematicsMathematicsDiscrete mathematicsBasis (linear algebra)Applied Mathematics010102 general mathematicssubdivision solverlinear programmingalgebraic systemsQuadratic function[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]Solver1991 Mathematics Subject Classification: 14Q15 14Q20 65G40Bernstein polynomialComputer Science Applications010101 applied mathematicsModeling and SimulationStandard basisGeometry and TopologyComputer Vision and Pattern RecognitionSoftwareInternational Journal of Shape Modeling
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