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Multi-quadric Radial Basis Function Interpolation


The multi-quadric radial basis function interpolation scheme attempt to represent Z as a function of X and Y using the following relation



where N is the number of data points used in the interpolation process, the w values are weighting factors. s is a relative smoothing parameter which is zero in the current implementation.  


The weights are found by solving the linear system of N equations that force the above equation to perfectly represent the provided data.  Once the weights are determined the equation is used to interpolate or extrapolate the values of Z for specified values of X and Y.  The computations needed to determine the weights are O(N cubed) so the computational effort increases significantly as N is increased.  The Interpolate2D function provides an optional argument to specify N.  If N is less than the number of data points, N points will be selected that are closest to Z in normalized coordinates.  N is128 by default.