Hyperinterpolation on the square

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:210

Article; Proceedings Paper

Caliari, Marco¹  De Marchi, Stefano²  Vianello, Marco¹ 

[1] Univ Padua, Dept Pure & Appl Math, I-35121 Padua, Italy

[2] Univ Verona, Dept Comp Sci, I-37100 Verona, Italy

关键词: hyperinterpolation;    square;    Xu points;    minimal cubature formulas;    Lebesgue constant;   

DOI  :  10.1016/j.cam.2006.10.058

来源: Elsevier

【 摘 要 】

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. (C) 2006 Published by Elsevier B.V.

【 授权许可】

Free