|
|
| |
| Spherical Scattered Data Quasi-interpolation by Gaussian Radial Basis Function |
| |
Citation： |
Zhixiang CHEN,Feilong CAO.Spherical Scattered Data Quasi-interpolation by Gaussian Radial Basis Function[J].Chinese Annals of Mathematics B,2015,36(3):401~412 |
| Page view： 1196
Net amount： 1175 |
Authors： |
Zhixiang CHEN; Feilong CAO; |
Foundation： |
supported by the National Natural Science Foundation of China (Nos. 61272023,
61179041). |
|
|
| Abstract： |
Since the spherical Gaussian radial function is strictly positive definite, the
authors use the linear combinations of translations of the Gaussian kernel to interpolate
the scattered data on spheres in this article. Seeing that target functions are usually outside
the native spaces, and that one has to solve a large scaled system of linear equations to
obtain combinatorial coefficients of interpolant functions, the authors first probe into some
problems about interpolation with Gaussian radial functions. Then they construct quasiinterpolation
operators by Gaussian radial function, and get the degrees of approximation.
Moreover, they show the error relations between quasi-interpolation and interpolation when
they have the same basis functions. Finally, the authors discuss the construction and
approximation of the quasi-interpolant with a local support function. |
Keywords： |
Scattered data, Approximation, Spherical Gaussian radial basis function,
Modulus of continuity |
Classification： |
41A17, 41A25, 41A63 |
|
|
Download PDF Full-Text
|
|
|
|
