Masjukov, A.
October 2007
Computational Methods in Applied Mathematics;2007, Vol. 7 Issue 4, p321
Academic Journal
For bivariate and trivariate interpolation we propose in this paper a set of integrable radial basis functions (RBFs). These RBFs are found as fundamental solutions of appropriate PDEs and they are optimal in a special sense. The condition number of the interpolation matrices as well as the order of convergence of the interpolation are estimated. Moreover, the proposed RBFs provide smooth approximations and approximate fulfillment of the interpolation conditions. This property allows us to avoid the undecidable problem of choosing the right scale parameter for the RBFs. Instead we propose an iterative procedure in which a sequence of improving approximations is obtained by means of a decreasing sequence of scale parameters in an a priori given range. The paper provides a few clear examples of the advantage of the proposed interpolation method.


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