Vector hyperinterpolation on the sphere
نویسندگان
چکیده
منابع مشابه
Hyperinterpolation on the sphere
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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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.
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This paper considers the problem of approximation of a continuous function on the unit sphere S ⊆ IR by a spherical polynomial from the space IPn of all spherical polynomials of degree ≤ n. For r = 3 it was shown in [16] that the hyperinterpolation approximation Lnf (which is the linear projection obtained by approximating the Fourier coefficients in the exact L2 orthogonal projection by a posi...
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Hyperinterpolation on the sphere, as introduced by Sloan in 1995, is a constructive approximation method which is favorable in comparison with interpolation, but still lacking in pointwise convergence in the uniform norm. For this reason we combine the idea of hyperinterpolation and of summation in a concept of generalized hyperinterpolation. This is no longer projectory, but convergent if a ma...
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This paper presents a new approach for Radial Basis Function (RBF) interpolation on a sphere. Standard approaches use the Euclidian metrics for the distance calculation of two points. However, for interpolation on a sphere, more naturally is computation of the distance as the shortest distance over the surface on a sphere, i.e. spherical distance of two points is more natural for interpolation ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2009
ISSN: 0021-9045
DOI: 10.1016/j.jat.2008.05.002