Optimal Centers’ Allocation in Smoothing or Interpolating with Radial Basis Functions

On Smoothing for Multilevel Approximation with Radial Basis Functions

In a recent paper with Jerome we have suggested the use of a smoothing operation at each step of the basic multilevel approximation algorithm to improve the convergence rate of the algorithm. In our original paper the smoothing was deened via convolution, and its actual implementation was done via numerical quadrature. In this paper we suggest a diierent approach to smoothing, namely the use of...

Approximation by Radial Basis Functions with Finitely Many Centers

Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that in...

MQ-Radial Basis Functions Center Nodes Selection with PROMETHEE Technique

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

Smoothing splines using compactly supported , positive definite , radial basis functions

In this paper, we develop a fast algorithm for a smoothing spline estimator in multivariate regression. To accomplish this, we employ general concepts associated with roughness penalty methods in conjunction with the theory of radial basis functions and reproducing kernel Hilbert spaces. It is shown that through the use of compactly supported radial basis functions it becomes possible to recove...

Optimal Distribution of Centers for Radial Basis Function Methods