Some Numerical Experiments for Determining the Optimal Value of the Scale Parameter for Meshfree Interpolation

Msc Alvin ASIMI; Prof.Dr LulÃ«zim HANELLI

Abstract

This paper consists in the compression of two methods for determining the optimal ï¥ parameter for the Meshfree interpolation of a data set. In the first part we will present two approaches: “Trial and Error” and “Leave one out” cross validation. In the second part are presented some 1D and 2D experiments for comparing this two approaches. For each approach, we will determine the optimal ï¥ scaling parameter for 1D and 2D interpolation with different values of N data points. At the end there will be a comparison between the results issued . We will use MATLAB for all the calculations and the plots. The data sites used in this paper can be downloaded at http://www.math.unipd.it/~demarchi/TAA2010/.

Keywords

Meshfree Interpolation, Trial and Error, Levae one out, Matlab, optimal ï¥ parameter.

Reference

[1] Schaback, R and Welland, H (2006). Kernel techniques: From machine learning to meshless methods, Acta Numerica, 15, pp. 543- 639.

[2] Rippa, S. (1999) An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv in Comput. Math. 11, pp. 193-210

[3] used data: http://www.math.unipd.it/~demarchi/TAA2010/

Cites this article as

M. A. A. , P. L. H. , "Some Numerical Experiments for Determining the Optimal Value of the Scale Parameter for Meshfree Interpolation", International Journal of Innovative Research in Engineering & Management (IJIREM), Vol-3, Issue-3, Page No-225-228, 2016. Available from: