Least squares surface approximation to scattered data using multiquadric functions
Franke, Richard H.
Nielson, Gregory M.
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This report documents an investigation into some methods for fitting surfaces to scattered data. The form of the fitting function is a multiquadric function with the criteria for the fit being the least mean squared resifual for the data points. The principal problem is the selection of knot points (or base points for the multiquadric basis functions), although the selection of the multiquadric parameter also plays a nontrivial role in the process. We first describe a greedy algorithm for knot selection, and this procedure is used as an initial step in what follows. The minimization including knot locations and multiquadric parameter is explored, with some unexpected results in terms of 'near repeated' knots. This phenomenon is explored, and leads us to consider variable parameter values for the basis functions. Examples and results are given throughout.
Approved for public release; distribution is unlimited.
NPS Report NumberNPS-MA-93-008
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