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

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 effici...

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Veröffentlicht in:Applied numerical mathematics Jg. 57; H. 3; S. 304 - 319
Hauptverfasser: Karageorghis, Andreas, Chen, C.S., Smyrlis, Yiorgos-Sokratis
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.03.2007
Elsevier
Schlagworte:
Boundary meshless methods
Circulant matrices
Elliptic boundary value problems
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical linear algebra
Partial differential equations
Radial basis functions
Sciences and techniques of general use
Elliptic boundary value problems
Radial basis functions
Boundary meshless methods
Circulant matrices
Function approximation
Numerical approximation
Radial basis function
Numerical analysis
Elliptic equation
Boundary value problem
Applied mathematics
Circulant matrix
Two-dimensional calculations
Large scale
Boundary meshless method
Block matrix
ISSN:0168-9274, 1873-5460
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Beschreibung
Zusammenfassung: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2006.03.028