Hyperinterpolation at Xu Points and Interpolation at Padua Points in the Square: Computational Aspects
نویسندگان
چکیده
منابع مشابه
Interpolation points and interpolation formulae on the square
The problem of choosing " good " nodes on a given compact set is a central one in multivariate polynomial interpolation. Besides unisolvence, which is by no means an easy problem, for practical purposes one needs slow growth of the Lebesgue constant and computational efficiency. In this talk, we present new sets of nodes recently studied for polynomial interpolation on the square that are asymp...
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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...
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We give a simple, geometric and explicit construction of bivariate interpolation at certain points in a square (called Padua points), giving compact formulas for their fundamental Lagrange polynomials. We show that the associated norms of the interpolation operator, i.e., the Lebesgue constants, have minimal order of growth of O((log n)2). To the best of our knowledge this is the first complete...
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The Padua points are the first known example of optimal points for total degree polynomial interpolation in two variables, with a Lebesgue constant increasing like log of the degree; cf. [1, 2, 3]. Moreover, they generate a nontensorial Clenshaw-Curtis-like cubature formula, which turns out to be competitive with the tensorial Gauss-Legendre formula and even with the few known minimal formulas ...
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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...
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