A Matrix Decomposition RBF Algorithm: Approximation of Functions and their Derivatives
Document Type
Article
Publication Date
3-1-2007
Department
Mathematics
School
Mathematics and Natural Sciences
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 algorithin is also capable of solving large-scale problems with more than 100 000 interpolation points in two dimensions. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.
Publication Title
Applied Numerical Mathematics
Volume
57
Issue
3
First Page
304
Last Page
319
Recommended Citation
Karageorghis, A.,
Chen, C.,
Smyrlis, Y.
(2007). A Matrix Decomposition RBF Algorithm: Approximation of Functions and their Derivatives. Applied Numerical Mathematics, 57(3), 304-319.
Available at: https://aquila.usm.edu/fac_pubs/2057