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Localization of subsets of discontinuity points of a noisy function

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Abstract

We consider an ill-posed problem of localization of discontinuities of the first kind of a one-dimensional function, when knowing only its approximation and the error level δ in the metric of L 2(−∞,+∞). We propose a new statement of the problem when all discontinuities are divisible into subsets, and the localization takes place for subsets of discontinuities. Assuming additionally that all discontinuities in each subset have jumps of one sign, we construct a new regular method that allows to determine the number of subsets of discontinuities, to approximate their boundaries, and to estimate the approximation accuracy.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia

    A. L. Ageev & T. V. Antonova

Authors
  1. A. L. Ageev
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  2. T. V. Antonova
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Corresponding author

Correspondence to A. L. Ageev.

Additional information

Original Russian Text © A.L. Ageev, T.V. Antonova, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 11, pp. 13–19.

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Ageev, A.L., Antonova, T.V. Localization of subsets of discontinuity points of a noisy function. Russ Math. 61, 10–15 (2017). https://doi.org/10.3103/S1066369X17110020

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  • DOI: https://doi.org/10.3103/S1066369X17110020

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