Hyperinterpolation in the cube

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

• Book ID: 104008117
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 323 KB
• Volume: 55
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2007.10.003

✦ Synopsis

We construct an hyperinterpolation formula of degree n in the three-dimensional cube, by using the numerical cubature formula for the product Chebyshev measure given by the product of a (near) minimal formula in the square with Gauss-Chebyshev-Lobatto quadrature. The underlying function is sampled at N ∼ n 3 /2 points, whereas the hyperinterpolation polynomial is determined by its (n + 1)(n + 2)(n + 3)/6 ∼ n 3 /6 coefficients in the trivariate Chebyshev orthogonal basis. The effectiveness of the method is shown by a numerical study of the Lebesgue constant, which turns out to increase like log 3 (n), and by the application to several test functions.