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Sib. Zh. Vychisl. Mat., 2012, Volume 15, Number 4, Pages 345–357 (Mi sjvm485)  

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

Localization method for lines of discontinuity of approximately defined function of two variables

T. V. Antonova

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

Abstract: A function of two variables with the lines of discontinuity of the first kind is considered. It is assumed that outside discontinuity lines the function to be measured is smooth and has a limited partial derivative. Instead of the accurate function its approximation in $L_2$ and perturbation level are known. The problem in question belongs to the class of nonlinear ill-posed problems, for whose solution it is required to construct regularizing algorithms. We propose a reduced theoretical approach to solving the problem of localizing the discontinuity lines of the function that is noisy in the space $L_2$. This is done in the case when conditions of an exact function are imposed “in the small”. Methods of averaging have been constructed, the estimations of localizing the line (in the small) have been obtained.

Key words: ill-posed problems, localization of singularities, line of discontinuity, regularization.

Full text: PDF file (254 kB)
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English version:
Numerical Analysis and Applications, 2012, 5:4, 285–296

UDC: 517.988.68
Received: 31.05.2011
Revised: 27.09.2011

Citation: T. V. Antonova, “Localization method for lines of discontinuity of approximately defined function of two variables”, Sib. Zh. Vychisl. Mat., 15:4 (2012), 345–357; Num. Anal. Appl., 5:4 (2012), 285–296

Citation in format AMSBIB
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\by T.~V.~Antonova
\paper Localization method for lines of discontinuity of approximately defined function of two variables
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
\issue 4
\pages 345--357
\mathnet{http://mi.mathnet.ru/sjvm485}
\elib{https://elibrary.ru/item.asp?id=20495040}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 4
\pages 285--296
\crossref{https://doi.org/10.1134/S1995423912040015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870459853}


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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, “Issledovanie porogovogo (korrelyatsionnogo) metoda i ego prilozhenie k lokalizatsii osobennostei”, Sib. elektron. matem. izv., 13 (2016), 829–848  mathnet  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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