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The sparse cardinal sine decomposition and its application for fast numerical convolution

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Abstract

Fast convolution algorithms on unstructured grids have become a well established subject. Algorithms such as Fast Multipole Method (FMM), Adaptive Cross Approximation (ACA) or \(\mathcal {H}\)-matrices for instance are, by now, classical and reduce the complexity of the matrix-vector product from O(N 2) to O(N log N) with a broad range of applications in e.g. electrostatics, magnetostatics, acoustics or electromagnetics. In this paper we describe a new algorithm of which we would like to explore the potential. Based on the Non Uniform FFT algorithm, it is at the same time simple, efficient and versatile.

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Authors and Affiliations

  1. CMAP - Ecole Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France

    François Alouges & Matthieu Aussal

  2. Digital Media Solutions, 45 Grande Allée du 12 Février 1934, 77186, Noisiel, France

    Matthieu Aussal

Authors
  1. François Alouges
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  2. Matthieu Aussal
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Correspondence to François Alouges.

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Alouges, F., Aussal, M. The sparse cardinal sine decomposition and its application for fast numerical convolution. Numer Algor 70, 427–448 (2015). https://doi.org/10.1007/s11075-014-9953-6

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  • DOI: https://doi.org/10.1007/s11075-014-9953-6

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