A Method for Selecting Shape Parameters in Multiquadric Radial Basis Function Interpolation and Its Application

The shape parameters of Multiquadric Radial Basis Function (MQ-RBF) have great influence on its interpolation effect. In this paper, the selection method of shape parameters is studied, and the Random Walk (RW) algorithm is used to determine the shape parameters of MQ-RBF. The principle and steps of parameter selection are given in detail, and the algorithm is tested from the aspects of interpolation effect, iteration times and operation time. Numerical experiments show that compared with other common methods, the algorithm significantly improves the interpolation accuracy of MQ-RBF while ensuring the parameter selection speed. Engineering examples also verify the effectiveness of the algorithm.