, Volume 11, Issue 2–3, pp 183–192

# Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions

• A.C. Faul
• M.J.D. Powell
Article

## Abstract

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.

## Keywords

Radial Basis Function Iterative Algorithm Interpolation Point Iterative Technique Thin Plate Spline
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## References

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