Interpolation by Radial Basis Functions on Sobolev Space
نویسندگان
چکیده
منابع مشابه
Interpolation by Radial Basis Functions on Sobolev Space
Interpolation by translates of suitable radial basis functions is an important approach towards solving the scattered data problem. However, for a large class of smooth basis functions (including multiquadrics f(x)=(|x|+l), m > d/2, 2m−d ̈ 2Z), the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximands. The approximands f need to b...
متن کاملSobolev-type Error Estimates for Interpolation by Radial Basis Functions
We generalize techniques dating back to Duchon 4] for error estimates for interpolation by thin plate splines to basis functions with positive and algebraically decaying Fourier transform. We include L p-estimates for 1 p < 2 that can also be applied to thin plate spline approximation. x1. Introduction Radial basis functions are a well-established tool for multivariate approximation problems. A...
متن کاملSpectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space
In this study, we are mainly interested in error estimates of interpolation, using smooth radial basis functions such as multiquadrics. The current theories of radial basis function interpolation provide optimal error bounds when the basis function φ is smooth and the approximand f is in a certain reproducing kernel Hilbert space Fφ. However, since the space Fφ is very small when the function φ...
متن کاملOn the Eeciency of Interpolation by Radial Basis Functions
We study the computational complexity, the error behavior, and the numerical stability of interpolation by radial basis functions. It turns out that these issues are intimately connected. For the case of compactly supported radial basis functions, we consider the possibility of getting reasonably good reconstructions of d-variate functions from N data at O(Nd) computational cost and give some s...
متن کاملApproximation of a Fuzzy Function by Using Radial Basis Functions Interpolation
In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...
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: 2001
ISSN: 0021-9045
DOI: 10.1006/jath.2001.3584