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
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.
ill-posed problem, regularizing algorithm, localization of singularities, discontinuity of the first kind.
PDF file (369 kB)
Journal of Applied and Industrial Mathematics, 2012, 6:3, 269–279
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
\by A.~L.~Ageev, T.~V.~Antonova
\paper Approximation of discontinuity lines of a~noisy function of two variables
\jour Sib. Zh. Ind. Mat.
\jour J. Appl. Industr. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
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, “Research of a threshold (correlation) method and application for localization of singularities”, Sib. Electron. Math. Rep., 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
|Number of views:|