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International Conference on Mathematical Methods for Curves and Surfaces

MMCS 2016: Mathematical Methods for Curves and Surfaces pp 233–250Cite as

Reconstructing Sparse Exponential Polynomials from Samples: Difference Operators, Stirling Numbers and Hermite Interpolation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10521))

Abstract

Prony’s method, in its various concrete algorithmic realizations, is concerned with the reconstruction of a sparse exponential sum from integer samples. In several variables, the reconstruction is based on finding the variety for a zero dimensional radical ideal. If one replaces the coefficients in the representation by polynomials, i.e., tries to recover sparse exponential polynomials, the zeros associated to the ideal have multiplicities attached to them. The precise relationship between the coefficients in the exponential polynomial and the multiplicity spaces are pointed out in this paper.

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Authors and Affiliations

  1. Lehrstuhl für Mathematik mit Schwerpunkt Digitale Bildverarbeitung & FORWISS, University of Passau, 94032, Passau, Germany

    Tomas Sauer

Authors
  1. Tomas Sauer
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Correspondence to Tomas Sauer .

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Editors and Affiliations

  1. University of Oslo, Oslo, Norway

    Michael Floater

  2. University of Oslo, Oslo, Norway

    Tom Lyche

  3. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  4. University of Oslo, Oslo, Norway

    Knut Mørken

  5. Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Sauer, T. (2017). Reconstructing Sparse Exponential Polynomials from Samples: Difference Operators, Stirling Numbers and Hermite Interpolation. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2016. Lecture Notes in Computer Science(), vol 10521. Springer, Cham. https://doi.org/10.1007/978-3-319-67885-6_13

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  • DOI: https://doi.org/10.1007/978-3-319-67885-6_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67884-9

  • Online ISBN: 978-3-319-67885-6

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