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Mixing symbolic and numerical approaches for the surface‐to‐surface intersection problem
Author(s) -
Fioravanti Mario,
GonzalezVega Laureano
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700884
Subject(s) - correctness , algebraic surface , computation , intersection (aeronautics) , surface (topology) , algebraic number , eigenvalues and eigenvectors , certificate , symbolic computation , algebra over a field , mixing (physics) , set (abstract data type) , computer science , mathematics , singular value decomposition , theoretical computer science , algorithm , pure mathematics , mathematical analysis , geometry , physics , quantum mechanics , engineering , programming language , aerospace engineering
This paper shows how the efficiency of the current methodologies applied to the surface‐to‐surface intersection problem can be improved by combining an algebraic/symbolic framework with efficient and robust numerical techniques. The algebraic/symbolic framework is used to translate the computation of resultants, subresultants, discriminants, etc. to one or several generalized eigenvalue problems and SVD computations. The framework requires only the values of the involved polynomials at some set of points, and it will guide the numerical computations, providing thus a certificate of the topological correctness of the output. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)