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Multivariate exponential analysis from the minimal number of samples

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Abstract

The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of samples down to the absolute minimum of (d + 1)n where d is the dimension of the problem and n is the number of exponential terms. To this end we present a fundamentally different approach for the multivariate problem statement. We combine a one-dimensional exponential analysis method such as ESPRIT, MUSIC, the matrix pencil or any Prony-like method, with some linear systems of equations because the multivariate exponents are inner products and thus linear expressions in the parameters.

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Acknowledgements

This work was partially supported by a Research Grant of the FWO-Flanders (Flemish Science Foundation).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp (CMI), Middelheimlaan 1, 2020, Antwerpen, Belgium

    Annie Cuyt & Wen-shin Lee

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  1. Annie Cuyt
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  2. Wen-shin Lee
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Correspondence to Wen-shin Lee.

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Communicated by: Yuesheng Xu

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Cuyt, A., Lee, Ws. Multivariate exponential analysis from the minimal number of samples. Adv Comput Math 44, 987–1002 (2018). https://doi.org/10.1007/s10444-017-9570-8

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  • DOI: https://doi.org/10.1007/s10444-017-9570-8

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