Some Numerical Experiments for Determining the Optimal Value of the Scale Parameter for Meshfree Interpolation
Msc Alvin ASIMI , Prof.Dr Lulëzim HANELLI
This paper consists in the compression of two methods for determining the optimal 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 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/.
Meshfree Interpolation, Trial and Error, Levae one out, Matlab, optimal parameter.
 Schaback, R and Welland, H (2006). Kernel techniques: From machine learning to meshless methods, Acta Numerica, 15, pp. 543- 639.
 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
 used data: http://www.math.unipd.it/~demarchi/TAA2010/
[Msc Alvin ASIMI , Prof.Dr Lulëzim HANELLI (2016) Some Numerical Experiments for Determining the Optimal Value of the Scale Parameter for Meshfree Interpolation IJIRCST Vol-3 Issue-3 Page No-225-228] (ISSN 2347 - 5552). www.ijircst.org
Msc Alvin ASIMI
Department of Mathematic Engineering, Polytechnic University of Tirana, Tirana, Albania