Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions
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Thin plate spline methods provide an interpolant to values of a real function and are highly useful in many applications. The need for iterative procedures arises, since hardly any sparsity occurs in the linear system of interpolation equations. This paper considers a generalization of the iterative algorithm developed by Beatson, Goodsell and Powell. A proof of convergence of this method is given. It depends mainly on the remark that all the changes to the thin plate spline coefficients reduce a certain semi‐norm of the difference between the required interpolant and the current approximation. The analysis applies also to analogous algorithms for other radial basis functions.
KeywordsRadial Basis Function Iterative Algorithm Interpolation Point Iterative Technique Thin Plate Spline
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