Constructive Polynomial Approximation on the Sphere
نویسندگان
چکیده
منابع مشابه
Filtered polynomial approximation on the sphere
Localised polynomial approximations on the sphere have a variety of applications in areas such as signal processing, geomathematics and cosmology. Filtering is a simple and effective way of constructing a localised polynomial approximation. In this thesis we investigate the localisation properties of filtered polynomial approximations on the sphere. Using filtered polynomial kernels and a speci...
متن کاملPolynomial approximation on the sphere using scattered data
We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space R, using samples of f at scattered sites. A central role is played by the construction of a new operator for polynomial approximation, which is a uniformly bounded quasi–projection in the de la Vallée Poussin style, i.e. it reproduces spherical polynomials up to ...
متن کاملSpherical Designs and Polynomial Approximation on the Sphere
This talk presents some joint work with An, Frommer, Lang, Sloan and Womersley on spherical designs and polynomial approximation on the sphere [1],[2],[4],[5]. Finding “good” finite sets of points on the unit sphere S in the Euclidean space R has been a hot research topic in mathematics, physics, and engineering for more than hundred years. There are several concepts of “good” finite sets of po...
متن کاملPolynomial frames on the sphere
We introduce a class of polynomial frames suitable for analyzing data on the surface of the unit sphere of a Euclidean space. Our frames consist of polynomials, but are well localized, and are stable with respect to all the Lp norms. The frames belonging to higher and higher scale wavelet spaces have more and more vanishing moments. 1 ∗The research of this author was supported, in part, by gran...
متن کاملAPPLIED MATHEMATICS REPORT AMR 98/19 Constructive Approximation on the Sphere
This paper considers the problem of constructive approximation of a continuous function on the unit sphere Sr−1 ⊆ Rr by a spherical polynomial from the space Pn of all spherical polynomials of degree ≤ n. In particular, for r = 3 it is shown that the hyperinterpolation approximation Lnf (in which the Fourier coefficients in the exact L2 orthogonal projection Pnf are approximated by a positive w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2000
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3426