Gaussian Cubature and Bivariate Polynomial Interpolation
نویسنده
چکیده
Gaussian cubature is used to study bivariate polynomial interpolation based on the common zeros of quasi-orthogonal polynomials.
منابع مشابه
On minimal cubature formulae for product weight functions 1
We derive in a simple way certain minimal cubature formulae, obtained by Morrow and Patterson [2], and Xu [4], using a different technique. We also obtain in explicit form new near minimal cubature formulae. Then, as a corollary, we get a compact expression for the bivariate Lagrange interpolation polynomials, based on the nodes of the cubature.
متن کاملA numerical code for fast interpolation and cubature at the Padua points
In this talk we discuss an efficient implementation in Matlab/Octave of bivariate interpolation and cubature at the so-called Padua points. Such points are the first known example of optimal points for total degree polynomial interpolation in two variables, with a Lebesgue constant increasing like log square of the degree; see [1, 2, 4, 5]. Moreover, the associated algebraic cubature formula ha...
متن کاملBivariate Lagrange interpolation at the Padua points: the ideal theory approach
The Padua points are a family of points on the square [−1, 1] 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 convergence of the inter...
متن کاملar X iv : 0 80 8 . 01 80 v 1 [ m at h . N A ] 1 A ug 2 00 8 CUBATURE FORMULA AND INTERPOLATION ON THE CUBIC DOMAIN
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [−1, 1], as well as new results on [−1, 1]. In particular, compact formulas for the fu...
متن کاملar X iv : 0 80 8 . 01 80 v 2 [ m at h . N A ] 1 5 A ug 2 00 8 CUBATURE FORMULA AND INTERPOLATION ON THE CUBIC DOMAIN
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [−1, 1], as well as new results on [−1, 1]. In particular, compact formulas for the fu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010