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
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.
ill-posed problems, localization of singularities, line of discontinuity, regularization.
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Numerical Analysis and Applications, 2012, 5:4, 285–296
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
\paper Localization method for lines of discontinuity of approximately defined function of two variables
\jour Sib. Zh. Vychisl. Mat.
\jour Num. Anal. Appl.
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This publication is cited in the following articles:
A. L. Ageev, T. V. Antonova, “O diskretizatsii metodov lokalizatsii osobennostei zashumlennoi funktsii”, Tr. IMM UrO RAN, 21, no. 1, 2015, 3–13
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
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
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
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
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
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
A. L. Ageev, T. V. Antonova, “O lokalizatsii negladkikh linii razryva funktsii dvukh peremennykh”, Tr. IMM UrO RAN, 25, no. 3, 2019, 9–23
A. L. Ageev, T. V. Antonova, “Novye otsenki tochnosti metodov lokalizatsii linii razryva zashumlennoi funktsii”, Sib. zhurn. vychisl. matem., 23:4 (2020), 351–364
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