Hyperinterpolation in the cube

Authors:
Marco Caliari;Stefano De Marchi;Marco Vianello
Affiliations:
Department of Computer Science, University of Verona, Italy;Department of Computer Science, University of Verona, Italy;Department of Pure and Applied Mathematics, University of Padua, Italy
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 11
Cited 1

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Abstract

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.