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Hyperinterpolation on the square

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

Book ID
104005315
Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
156 KB
Volume
210
Category
Article
ISSN
0377-0427

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✦ Synopsis

We show that hyperinterpolation at (near) minimal cubature points for the product Chebyshev measure, along with Xu compact formula for the corresponding reproducing kernel, provide a simple and powerful polynomial approximation formula in the uniform norm on the square. The Lebesgue constant of the hyperinterpolation operator grows like log 2 of the degree, as that of quasi-optimal interpolation sets recently proposed in the literature. Moreover, we give an accurate implementation of the hyperinterpolation formula with linear cost in the number of cubature points, and we compare it with interpolation formulas at the same set of points.

πŸ“œ SIMILAR VOLUMES

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dedicated to professor dr. dr. h. c. karl zeller on the occasion of his 75th birthday We investigate hyperinterpolation operators based on positive weighted quadrature rules, as introduced by Ian H. Sloan. If the rules are exact of double degree then, independently of the number of their nodes, the