Bivariate Lagrange interpolation at the Padua points: the ideal theory approach |
| |
Authors: | Len Bos Stefano De Marchi Marco Vianello Yuan Xu |
| |
Affiliation: | (1) Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada, T2N1N4;(2) Department of Computer Science, University of Verona, 37134, Verona, Italy;(3) Department of Pure and Applied Mathematics, University of Padua, 35131 Padua, Italy;(4) Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA |
| |
Abstract: | The Padua points are a family of points on the square [−1, 1]2 given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. Interpolation polynomials and cubature formulas based on the Padua points are studied from an ideal theoretic point of view, which leads to the discovery of a compact formula for the interpolation polynomials. The L p convergence of the interpolation polynomials is also studied. S. De Marchi and M. Vianello were supported by the “ex-60%” funds of the University of Padua and by the INdAM GNCS (Italian National Group for Scientific Computing). Y. Xu was partially supported by NSF Grant DMS-0604056. |
| |
Keywords: | 41A05 41A10 |
本文献已被 SpringerLink 等数据库收录! |
|