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The modified moment problem in the presence of noise

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Approximation Theory and its Applications

Abstract

The modified moment problem is little studied in the literature with respect to the classical moment problem due to the lacking of experiments measuring modified moments. The modified moment problem is analyzed in this paper, when noise affects the modified moments themselves. A numerical method for solving the problem, based on regularization, is given, together with a full theoretical analysis, convergence results and an optimized algorithm. The modified moment problem reveals strongly superior to the classical moment problem in terms of the amplification of the error, conditioning of the matrices involved and ease of computation.

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Authors and Affiliations

  1. Istituto per Applicazioni della Matematica CNR, Napoli, Italy

    U. Amato & M. F. Carfora

  2. Istituto per le Metodologie Avanzate di Analisi Ambientale CNR, Tito (PZ), Italy

    M. F. Carfora

Authors
  1. U. Amato
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  2. M. F. Carfora
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Amato, U., Carfora, M.F. The modified moment problem in the presence of noise. Approx. Theory & its Appl. 9, 50–70 (1993). https://doi.org/10.1007/BF02836270

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  • DOI: https://doi.org/10.1007/BF02836270

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