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Computing high precision Matrix Padé approximants

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Abstract

We describe a new method of computing matrix Padé approximants of series with integer data in an efficient and fraction-free way, by controlling the growth of the size of intermediate coefficients. This algorithm is applied to compute high precision Padé approximants of matrix-valued generating functions of time series. As an illustration we show that we can successfully recover from noisy equidistant sampling data a joint damped signal of four antenna, even in the presence of background signals.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé UMR CNRS 8524 (ANO-EDP), UFR Mathématiques – M3, UST Lille, 59655, Villeneuve d’Ascq Cedex, France

    Bernhard Beckermann

  2. Department of Physics, Texas Southern University, Houston, TX, USA

    Daniel Bessis, Luca Perotti & Daniel Vrinceanu

Authors
  1. Bernhard Beckermann
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  2. Daniel Bessis
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  3. Luca Perotti
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  4. Daniel Vrinceanu
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Corresponding author

Correspondence to Bernhard Beckermann.

Additional information

Dedicated to Claude Brezinski on the occasion of his 70th birthday.

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Beckermann, B., Bessis, D., Perotti, L. et al. Computing high precision Matrix Padé approximants. Numer Algor 61, 189–208 (2012). https://doi.org/10.1007/s11075-012-9596-4

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  • DOI: https://doi.org/10.1007/s11075-012-9596-4

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