Determining optimal value of the shape parameter $c$ in RBF for unequal distances topographical points by Cross-Validation algorithm

Document Type : Research Article


Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran


Several radial basis function based methods contain a free shape parameter which has  a crucial role in the accuracy of the methods. Performance evaluation of this parameter in different  functions with various data has always been a topic of study. In the present paper, we consider studying the methods which determine an optimal value for the shape parameter in interpolations of radial basis  functions for data collections produced by topographical images that are not necessarily in equal distances.  The Cross-Validation method is picked out of several existing algorithms proposed for determining the shape parameter.