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Optimal shift parameters for periodic spline interpolation

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Abstract

Using the exponential Euler spline, restricted on the unit circle, we sketch a unified approach to the periodic spline interpolation with shifted interpolation nodes. Mainly we are interested in the optimal choice of the shift parameter τ such that the corresponding interpolatory matrix possesses minimal condition or such that the related interpolation operator has minimal norm. We show that τ=0 is optimal in both cases. This improves known results of Merz, Reimer-Siepmann and Richards.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Rostock, D-18051, Rostock, Germany

    Gerlind Plonka

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  1. Gerlind Plonka
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Communicated by C.A. Micchelli

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Plonka, G. Optimal shift parameters for periodic spline interpolation. Numer Algor 6, 297–316 (1994). https://doi.org/10.1007/BF02142676

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  • DOI: https://doi.org/10.1007/BF02142676

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