Structured matrices in the application of bivariate interpolation to curve implicitization

Ana Marco and José-Javier Martínez

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 73, issue 6, 378-385

Abstract: A non-standard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered, and their respective computational complexities are analyzed. Although the techniques employed are usually associated to numerical analysis, in this case all the computations are carried out using exact rational arithmetic. The power of the Kronecker product of matrices in this application is stressed.

Keywords: Interpolation; Vandermonde matrix; Kronecker product; Computer aided geometric design; Resultant (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:73:y:2007:i:6:p:378-385

DOI: 10.1016/j.matcom.2006.07.001

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