0000000000393053

AUTHOR

D. Michelucci

showing 2 related works from this author

The Bernstein Basis and its applications in solving geometric constraint systems

2012

International audience; This article reviews the properties of Tensorial Bernstein Basis (TBB) and its usage, with interval analysis, for solving systems of nonlinear, univariate or multivariate equations resulting from geometric constraints. TBB are routinely used in computerized geometry for geometric modelling in CAD-CAM, or in computer graphics. They provide sharp enclosures of polynomials and their derivatives. They are used to reduce domains while preserving roots of polynomial systems, to prove that domains do not contain roots, and to make existence and uniqueness tests. They are compatible with standard preconditioning methods and fit linear program- ming techniques. However, curre…

Algebraic systems[ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA]Univariate and multivariate polynomials[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]Geometric constraint solving. Bernstein polytopeTensorial Bernstein basis
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On the Complexity of the Bernstein Combinatorial Problem

2012

International audience

combinatorial complexity[ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA][INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]interval arithmeticsBernstein polynomials[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]tensorial Bernstein basisComputingMilieux_MISCELLANEOUS
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