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On interpolation of smooth processes and functions

  • Methods of Signal Processing
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Abstract

We consider interpolation problems for smooth stationary Gaussian processes and functions from Sobolev classes. These problems are shown to be closely related. Much attention is paid to spline-based interpolation methods. In particular, we prove that splines are limiting optimal interpolations of stationary Gaussian processes with special spectral densities. Based on this analogy, we propose a simple method for controlling accuracy of spline interpolation.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    G. K. Golubev

  2. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    G. K. Golubev

  3. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    E. A. Krymova

Authors
  1. G. K. Golubev
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  2. E. A. Krymova
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Correspondence to G. K. Golubev.

Additional information

Original Russian Text © G.K. Golubev, E.A. Krymova, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 2, pp. 34–57.

Supported in part by the Laboratory of Structural Methods of Data Analysis in Predictive Modeling, Faculty of Control and Applied Mathematics, Moscow Institute of Physics and Technology, under the Government of Russian Federation grant, project no. 11.G34.31.0073.

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Golubev, G.K., Krymova, E.A. On interpolation of smooth processes and functions. Probl Inf Transm 49, 127–148 (2013). https://doi.org/10.1134/S0032946013020038

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  • DOI: https://doi.org/10.1134/S0032946013020038

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