Positive Approximation and Interpolation Using Compactly Supported Radial Basis Functions
نویسندگان
چکیده
We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the proposed method is flexible.
منابع مشابه
Compactly supported radial basis functions : how and why ? by Sheng - Xin
The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an accepted method for machine learning, one of the foundations of mesh-free methods, an alternative way to construct higher order methods for solving partial differential equations (PDEs), an emerging method for solving PDEs on surfaces, ...
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 کاملAn Image Inpainting Algorithm Based on CSRBF Interpolation
In this paper, we propose a novel algorithm for image inpainting based on compactly supported radial basis functions (CSRBF) interpolation. The algorithm converts 2D image inpainting problem into implict surface reconstruction problem from 3D points set. Firstly, we construct the implicit surface for approximating the points set which convert from damaged image by using radial basis functions (...
متن کاملError Estimates for Interpolation by Compactly Supported Radial Basis Functions of Minimal Degree
We consider error estimates for the interpolation by a special class of compactly supported radial basis functions. These functions consist of a univariate polynomial within their support and are of minimal degree depending on space dimension and smoothness. Their associated \native" Hilbert spaces are shown to be norm-equivalent to Sobolev spaces. Thus we can derive approximation orders for fu...
متن کاملCollocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the pr...
متن کامل