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Structured matrix methods for CAGD: an application to computing the resultant of polynomials in the Bernstein basis
Author(s) -
Bini Dario A.,
Gemignani Luca,
Winkler Joab R.
Publication year - 2005
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.444
Subject(s) - bézier curve , bernstein polynomial , mathematics , gaussian elimination , computation , matrix (chemical analysis) , intersection (aeronautics) , symbolic computation , domain (mathematical analysis) , algebra over a field , algorithm , gaussian , pure mathematics , geometry , mathematical analysis , physics , quantum mechanics , engineering , aerospace engineering , materials science , composite material
We devise a fast fraction‐free algorithm for the computation of the triangular factorization of Bernstein–Bezoutian matrices with entries over an integral domain. Our approach uses the Bareiss fraction‐free variant of Gaussian elimination, suitably modified to take into account the structural properties of Bernstein–Bezoutian matrices. The algorithm can be used to solve problems in algebraic geometry that arise in computer aided geometric design and computer graphics. In particular, an example of the application of this algorithm to the numerical computation of the intersection points of two planar rational Bézier curves is presented. Copyright © 2005 John Wiley & Sons, Ltd.