Error estimates for scattered data interpolation on spheres
نویسندگان
چکیده
منابع مشابه
Error estimates for scattered data interpolation on spheres
We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics....
متن کاملStability results for scattered-data interpolation on Euclidean spheres
The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the separation distance of the sampling nodes and on the degree of polynomials being used. To this end, we establish a packing argument for well separated sampling nodes and construct strongly localized polynomials on ...
متن کاملScattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
In this paper we present error estimates for kernel interpolation at scattered sites on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on Rd, such as radial basis functions, to a smooth, compact embedded submanifold M ⊂ Rd with no boundary. For restricted kernels having finite smoothness, we provide a complete characterization of the native s...
متن کاملLocal Error Estimates for Radial Basis Function Interpolation of Scattered Data
Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions (r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain \Kriging function", which allows a formulation as an integral involving the Fourier transform of. The explicit construction of locally well{behaving adm...
متن کاملScattered data approximation of fully fuzzy data by quasi-interpolation
Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$. In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...
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: Mathematics of Computation
سال: 1999
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-99-01080-7