Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...

Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only non-oscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as their limiting case) leads to non-singular interpolants with in...

This paper discusses application of the piecewise sinusoidal (PWS) basis function (BF) over a chain of several wire segments, i.e. as a multiple domain basis functions. The usage of PWS BF is compared to results based on the piecewise linear (PWL) basis functions. An example of meander monopole demonstrates the advantages associated with the PWS BF.

In this paper, we construct a set of non-polynomial basis functions from a generalised Birkhoff interpolation problem involving the operator: Lλ = d2/dx2 − λ2 with constant λ. With a direct inverting the operator, the basis can be pre-computed in a fast and stable manner. This leads to new collocation schemes for general second-order boundary value problems with (i) the matrix corresponding to ...

The N basis functions are typically chosen so that Surface reflectance functions(SRFs) and spectral power distributions (SPDs) can be accurately reconstructed from their N-dimensional vector codes. Typical rendering applications assume that the resulting mapping is an isomorphism where vector operations of addition, scalar multiplication, component-wise multiplication on the N-vectors can be us...

The selection of the spatial basis functions is very important for model reduction of the nonlinear partial differential equations (PDEs) under time/space separation framework, which will significantly affect the accuracy and efficiency of the modeling. Using the spatial basis functions expansions and the Galerkin method, the finite-dimensional ordinary differential equation (ODE) systems can b...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...