Bivariate Lagrange interpolation at the Padua points: Computational aspects

✍ Scribed by Marco Caliari; Stefano De Marchi; Marco Vianello

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 370 KB
• Volume: 221
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.10.027

✦ Synopsis

The so-called "Padua points" give a simple, geometric and explicit construction of bivariate polynomial interpolation in the square. Moreover, the associated Lebesgue constant has minimal order of growth O(log 2 (n)). Here we show four families of Padua points for interpolation at any even or odd degree n, and we present a stable and efficient implementation of the corresponding Lagrange interpolation formula, based on the representation in a suitable orthogonal basis. We also discuss extension of (nonpolynomial) Padua-like interpolation to other domains, such as triangles and ellipses; we give complexity and error estimates, and several numerical tests.