A matrix decomposition RBF algorithm: Approximation of functions and their derivatives

Authors:
Andreas Karageorghis;C. S. Chen;Yiorgos-Sokratis Smyrlis
Affiliations:
Department of Mathematics and Statistics, University of Cyprus/ΠANEΠIΣTHMIO KYΠPOY, PO Box 20537, 1678 Nicosia/ΛEYKΩΣIA, Cyprus/KYΠPOΣ;Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA;Department of Mathematics and Statistics, University of Cyprus/ΠANEΠIΣTHMIO KYΠPOY, PO Box 20537, 1678 Nicosia/ΛEYKΩΣIA, Cyprus/KYΠPOΣ
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 8
Cited 3

Radial basis function approximations as smoothing splines

Applied Mathematics and Computation
Matrix analysis and applied linear algebra

Matrix analysis and applied linear algebra
A new class of radial basis functions with compact support

Mathematics of Computation
Some Aspects of the Method of Fundamental Solutions for Certain Harmonic Problems

Journal of Scientific Computing
Computational test of approximation of functions and their derivatives by radial basis functions

Neural, Parallel & Scientific Computations
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods

SIAM Journal on Scientific Computing
Overlapping domain decomposition method by radial basis functions

Applied Numerical Mathematics
Radial Basis Functions

Radial Basis Functions

Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains

Journal of Computational and Applied Mathematics
Multi-level meshless methods based on direct multi-elliptic interpolation

Journal of Computational and Applied Mathematics
Efficient MFS Algorithms for Inhomogeneous Polyharmonic Problems

Journal of Scientific Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

We propose an efficient algorithm for the approximation of functions and their derivatives using radial basis functions (RBFs). The interpolation points are placed on concentric circles and the resulting matrix has a block circulant structure. We exploit this circulant structure to develop an efficient algorithm for the solution of the resulting system using RBFs. As a result, extremely high accuracy in approximating the given function and its derivatives can be achieved. The given algorithm is also capable of solving large-scale problems with more than 100@?000 interpolation points in two dimensions.