THE PARAMETER R2 IN MULTIQUADRIC INTERPOLATION

The multiquadric (MQ) method is an effective bivariate interpolant to three-dimensional data (x(i), y(i), z(i)), where the (x(i), y(i)) are arbitarily located in the plane. The accuracy of the MQ method is dependent on a user defined parameter R2, and most practitioners select R2 based upon the number of data points and the locations of the (x(i), y(i)) in the plane. We observe that the optimal value of R2 is a strong function of the z(i), and that it is essentially independent of both the number and the locations of the (x(i), y(i)) points. Contrary to some opinions, we observe that the MQ method can effectively interpolate to "track data," that is, data sampled densely along tracks in the plane. Together with several other observations, we present an algorithm that generally yields an effective value for R2.