Structured matrices in the application of bivariate interpolation to curve implicitization
- 作者：Ana Marco ; José ; -Javier Martí ; nez
- 关键词：Interpolation ; Vandermonde matrix ; Kronecker product ; Computer aided geometric design ; Resultant
- 刊名：Mathematics and Computers in Simulation
- 出版年：2007
- 期刊代码：88_03784754
- 类别：cp
- 出版时间：6 February 2007
- 卷：73
- 期：6
- 页码：378-385
- 文件大小：150 K
摘要
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.