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 Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 1, Pages 44–58 (Mi timm203)

Regularizing algorithms for localizing the breakpoints of a noisy function

T. V. Antonova

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

Abstract: We consider the problem of localizing the singularities (breakpoints) of functions that are noisy in the spaces $L_p$, $1<p<\infty$, or $C$. We construct a wide class of smoothing algorithms that determine the number and location of breakpoints. In addition, for the case when a function is noisy in $C$, a finitedifference method is constructed. For the proposed methods, convergence theorems are proved and approximation accuracy estimates for the location of breakpoints are obtained. The lower estimates obtained in this paper show the order-optimality of the methods. For all the methods constructed, their capacity of separating close breakpoints is investigated.

Keywords: ill-posed problems, localization of breakpoints, regularizing algorithms, separability threshold

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 265, suppl. 1, S24–S39

Bibliographic databases:

UDC: 517.988.68

Citation: T. V. Antonova, “Regularizing algorithms for localizing the breakpoints of a noisy function”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 44–58; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S24–S39

Citation in format AMSBIB
\Bibitem{Ant09} \by T.~V.~Antonova \paper Regularizing algorithms for localizing the breakpoints of a~noisy function \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2009 \vol 15 \issue 1 \pages 44--58 \mathnet{http://mi.mathnet.ru/timm203} \elib{http://elibrary.ru/item.asp?id=11929776} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2009 \vol 265 \issue , suppl. 1 \pages S24--S39 \crossref{https://doi.org/10.1134/S0081543809060030} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000268192700003} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. T. V. Antonova, “New methods for localizing discontinuities of a noisy function”, Num. Anal. Appl., 3:4 (2010), 306–316
2. A. L. Ageev, T. V. Antonova, “A method for the localization of singularities of a solution to a convolution-type equation of the first kind with a step kernel”, Russian Math. (Iz. VUZ), 55:7 (2011), 1–8
3. A. L. Ageev, T. V. Antonova, “O nekorrektno postavlennykh zadachakh lokalizatsii osobennostei”, Tr. IMM UrO RAN, 17, no. 3, 2011, 30–45
4. Kurlikovskii D.V., Ageev A.L., Antonova T.V., “Research of a Threshold (Correlation) Method and Application For Localization of Singularities”, Sib. Electron. Math. Rep., 13 (2016), 829–848
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