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Sib. Zh. Ind. Mat., 2012, Volume 15, Number 1, Pages 3–13 (Mi sjim705)  

This article is cited in 9 scientific papers (total in 9 papers)

Approximation of discontinuity lines of a noisy function of two variables

A. L. Ageev, T. V. Antonova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, RUSSIA

Abstract: We construct and study methods for localizing (determining the location) a line in whose neighborhood the function of two variables in question is smooth while having discontinuity of the first kind along the line. Instead of the exact function, an approximation in $L_2$ is available with a known noise level. This problem belongs to the class of ill-posed nonlinear problems and, in order to solve it, we have to construct regularizing algorithms. We propose a simplified theoretical approach to the problem of discontinuity line localization for a noisy function with conditions on the exact function imposed in an arbirarily thin strip crossing the discontinuity line. We construct averaging methods and estimate the precision of localization for them.

Keywords: ill-posed problem, regularizing algorithm, localization of singularities, discontinuity of the first kind.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:3, 269–279

Bibliographic databases:

UDC: 517.988.68
Received: 30.06.2011

Citation: A. L. Ageev, T. V. Antonova, “Approximation of discontinuity lines of a noisy function of two variables”, Sib. Zh. Ind. Mat., 15:1 (2012), 3–13; J. Appl. Industr. Math., 6:3 (2012), 269–279

Citation in format AMSBIB
\Bibitem{AgeAnt12}
\by A.~L.~Ageev, T.~V.~Antonova
\paper Approximation of discontinuity lines of a~noisy function of two variables
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 1
\pages 3--13
\mathnet{http://mi.mathnet.ru/sjim705}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3112331}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 269--279
\crossref{https://doi.org/10.1134/S1990478912030015}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. L. Ageev, T. V. Antonova, “O diskretizatsii metodov lokalizatsii osobennostei zashumlennoi funktsii”, Tr. IMM UrO RAN, 21, no. 1, 2015, 3–13  mathnet  mathscinet  elib
    2. A. L. Ageev, T. V. Antonova, “Methods for the approximating the discontinuity lines of a noisy function of two variables with countably many singularities”, J. Appl. Industr. Math., 9:3 (2015), 297–305  mathnet  crossref  crossref  mathscinet  elib
    3. A. L. Ageev, T. V. Antonova, “Discretization of a new method for localizing discontinuity lines of a noisy two-variable function”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 4–13  mathnet  crossref  crossref  mathscinet  isi  elib
    4. D. V. Kurlikovskii, A. L. Ageev, T. V. Antonova, “Research of a threshold (correlation) method and application for localization of singularities”, Sib. Electron. Math. Rep., 13 (2016), 829–848  crossref  isi
    5. A. L. Ageev, T. V. Antonova, “High accuracy algorithms for approximation of discontinuity lines of a noisy function”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 1–11  mathnet  crossref  crossref  isi  elib
    6. A. L. Ageev, T. V. Antonova, “A discrete algorithm for the localization of lines of discontinuity of a two-variable function”, J. Appl. Industr. Math., 11:4 (2017), 463–471  mathnet  crossref  crossref  elib
    7. A. L. Ageev, T. V. Antonova, “K voprosu o globalnoi lokalizatsii linii razryva funktsii dvukh peremennykh”, Tr. IMM UrO RAN, 24, no. 2, 2018, 12–23  mathnet  crossref  elib
    8. A. L. Ageev, T. V. Antonova, “O lokalizatsii negladkikh linii razryva funktsii dvukh peremennykh”, Tr. IMM UrO RAN, 25, no. 3, 2019, 9–23  mathnet  crossref  elib
    9. A. L. Ageev, T. V. Antonova, “Novye otsenki tochnosti metodov lokalizatsii linii razryva zashumlennoi funktsii”, Sib. zhurn. vychisl. matem., 23:4 (2020), 351–364  mathnet  crossref
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