Compactly Supported Radial Basis Functions for Function Interpolation: Comparative Behaviour

Fernando C. M. Menandro, Carlos F. Loeffler Neto, Hipólito J. S. G. Meira, Raphael P. R. Bastos


The use of compactly supported radial basis functions (CSRBFs) for interpolation of known functions in different methods in engineering is widespread. In this work a comprehensive comparative analysis was undertaken, using the root mean square error, for different weighed residual techniques and different Radial Basis Functions (RBFs). Interpolation was carried out in one and two dimensions by point collocation, point least-squares summation, and integral Galerkin method. The tested functions were taken from literature and cover most of the published functions. The results are presented in convergence plots which show the root mean square error against the number of RBFs taken. The results demonstrate convergence of the studied functions. It can be concluded from the results that some functions behave better than others in particular problems.

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