The Radial Basis Function shape parameter chosen and its application in engneering

Abstract

The shape parameter is proved to have great influence on Radial Basis Function (RBF) interpolation. Its impacts on Multiquadric (MQ) RBF are studied in this paper. Observation suggests that a large shape parameter improves the accuracy of the approximation of high non linear problems, but may lead to Runge Phenomenon (RP). This paper proposed an algorithm to obtain the shape parameter by minimizing the cross-valid error while controlling the RP. Compared with Kriging, numerical experiments show that the MQ RBF with optimum shape parameter can achieve higher accuracy when approximate the high non linear problems, the application in the engineering problems also proved the effectiveness of the algorithm.