Nonstationary Wavelets on them-Sphere for Scattered Data
نویسندگان
چکیده
منابع مشابه
Nonstationary Wavelets on the m - Spherefor Scattered
We construct classes of nonstationary wavelets generated by what we call spherical basis functions (SBFs), which comprise a subclass of Schoen-berg's positive deenite functions on the m-sphere. The wavelets are intrinsically deened on the m-sphere, and are independent of the choice of coordinate system. In addition, they may be orthogonalized easily, if desired. We will discuss decomposition, r...
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We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics, tensor-product spaces on a rectangular map of the sphere, functions deened over spherical triangulations, spherical splines, spherical radial basis functions, and some associated multi-resolution met...
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Spaces of polynomial splines deened on planar triangulations are very useful tools for tting scattered data in the plane. Recently, 4, 5], using homogeneous polynomials, we have developed analogous spline spaces deened on triangulations on the sphere and on sphere-like surfaces. Using these spaces, it is possible to construct analogs of many of the classical interpolation and tting methods. Her...
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Recently, fast and reliable algorithms for the evaluation of spherical harmonic expansions have been developed. The corresponding sampling problem is the computation of Fourier coefficients of a function from sampled values at scattered nodes. We consider a least squares approximation to and an interpolation of given data. Our main result is that the rate of convergence of the two proposed iter...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 1996
ISSN: 1063-5203
DOI: 10.1006/acha.1996.0025