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Computational Aspects of Approximation to Scattered Data by Using ‘Shifted’ Thin-Plate Splines

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Abstract

A new multivariate approximation scheme to scattered data on arbitrary bounded domains in R d is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the ‘shifted’ thin-plate spline (‘essentially,’ since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless data, but its main advantage seems to be in the former case. We suggest an algorithm for the new approximation scheme with a detailed description (in a MATLAB-like program). Some numerical examples are presented along with comparisons with thin-plate spline interpolation and Wahba's thin-plate smoothing spline approximation.

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  1. Department of Applied Mathematics, School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv, Tel-Aviv, 69978, Israel

    Jungho Yoon

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  1. Jungho Yoon
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Yoon, J. Computational Aspects of Approximation to Scattered Data by Using ‘Shifted’ Thin-Plate Splines. Advances in Computational Mathematics 14, 329–359 (2001). https://doi.org/10.1023/A:1012205804632

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