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Iterative polynomial interpolation and data compression

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Abstract

In this paper we look at some iterative interpolation schemes and investigate how they may be used in data compression. In particular, we use the pointwise polynomial interpolation method to decompose discrete data into a sequence of difference vectors. By compressing these differences, one can store an approximation to the data within a specified tolerance using a fraction of the original storage space (the larger the tolerance, the smaller the fraction).

We review the iterative interpolation scheme, describe the decomposition algorithm and present some numerical examples. The numerical results are that the best compression rate (ratio of non-zero data in the approximation to the data in the original) is often attained by using cubic polynomials and in some cases polynomials of higher degree.

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Author notes

  1. Morten DÆhlen

    Present address: Institutt for Informatikk, University of Oslo, Blindern, P.O. Box 1080, 0316, Oslo, Norway

Authors and Affiliations

  1. SINTEF-SI, Blindern, P. O. Box 124, 0314, Oslo, Norway

    Morten DÆhlen & Michael Floater

Authors
  1. Morten DÆhlen
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  2. Michael Floater
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Additional information

This work was supported by The Royal Norwegian Council for Scientific and Industrial Research (NTNF).

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DÆhlen, M., Floater, M. Iterative polynomial interpolation and data compression. Numer Algor 5, 165–177 (1993). https://doi.org/10.1007/BF02215679

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