Hyperinterpolation in the cube
نویسندگان
چکیده
منابع مشابه
Hyperinterpolation in the cube
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/2 points, whereas the hyperinterpolation polynomial is determined by its (n + 1)(n + 2)(n...
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In this paper we survey hyperinterpolation on the sphere Sd, d ≥ 2. The hyperinterpolation operator Ln is a linear projection onto the space Pn(S) of spherical polynomials of degree≤ n, which is obtained from L2(S)-orthogonal projection onto Pn(S) by discretizing the integrals in the L2(S) inner products by a positive-weight numerical integration rule of polynomial degree of exactness 2n. Thus ...
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We obtain upper bounds for Lebesgue constants (uniform norms) of hyperinterpolation operators via estimates for (the reciprocal of) Christoffel functions, with different measures on the disk and ball, and on the square and cube. As an application, we show that the Lebesgue constant of total-degree polynomial interpolation at the Morrow-Patterson minimal cubature points in the square has an O(de...
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It is shown that second-order results can be attained by the generalized hyperinterpolation operators on the sphere, which gives an affirmative answer to a question raised by Reimer in Constr. Approx. 18(2002), no. 2, 183–203.
متن کاملNew cubature formulae and hyperinterpolation
A new algebraic cubature formula of degree 2n + 1 for the product Chebyshev measure in the d-cube with ≈ nd/2d−1 nodes is established. The new formula is then applied to polynomial hyperinterpolation of degree n in three variables, in which coefficients of the product Chebyshev orthonormal basis are computed by a fast algorithm based on the 3dimensional FFT. Moreover, integration of the hyperin...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2008
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2007.10.003