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Structured matrices in the application of bivariate interpolation to curve implicitization

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  • Marco, Ana
  • Martínez, José-Javier

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.

Suggested Citation

  • Marco, Ana & Martínez, José-Javier, 2007. "Structured matrices in the application of bivariate interpolation to curve implicitization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 378-385.
    • Handle: RePEc:eee:matcom:v:73:y:2007:i:6:p:378-385
    DOI: 10.1016/j.matcom.2006.07.001
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    References listed on IDEAS

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    1. Blochinger, Wolfgang & Küchlin, Wolfgang & Ludwig, Christoph & Weber, Andreas, 1999. "An object-oriented platform for distributed high-performance symbolic computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(3), pages 161-178.
    2. Chiasson, John & Tolbert, Leon & McKenzie, Keith & Du, Zhong, 2003. "Real-time computer control of a multilevel converter using the mathematical theory of resultants," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(3), pages 197-208.
    3. Botana, Francisco & Valcarce, José L., 2004. "Automatic determination of envelopes and other derived curves within a graphic environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(1), pages 3-13.
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