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

• Autores: Andreas Karageorghis, C. S. Chen, Yiorgos-Sokratis Smyrlis
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 57, Nº. 3, 2007, págs. 304-319
• Idioma: inglés
• DOI: 10.1016/j.apnum.2006.03.028
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• Resumen

  • 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.