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Sib. Zh. Vychisl. Mat., 1999, Volume 2, Number 4, Pages 385–394 (Mi sjvm349)  

This article is cited in 13 scientific papers (total in 13 papers)

On representation of piecewise-smooth functions by rapidly convergent trigonometric series

V. V. Smelov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A specific variant of expansions of smooth and piecewise-smooth functions to rapidly convergent series with respect to trigonometric functions is suggested. This result is the basis for the effective approximations of the above-mentioned functions.

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Bibliographic databases:
UDC: 518.12+519.34
Received: 30.03.1999
Revised: 27.05.1999

Citation: V. V. Smelov, “On representation of piecewise-smooth functions by rapidly convergent trigonometric series”, Sib. Zh. Vychisl. Mat., 2:4 (1999), 385–394

Citation in format AMSBIB
\Bibitem{Sme99}
\by V.~V.~Smelov
\paper On representation of piecewise-smooth functions by rapidly convergent trigonometric series
\jour Sib. Zh. Vychisl. Mat.
\yr 1999
\vol 2
\issue 4
\pages 385--394
\mathnet{http://mi.mathnet.ru/sjvm349}
\zmath{https://zbmath.org/?q=an:0939.42001}


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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. V. V. Smelov, “Lokalnyi algoritm gladkoi approksimatsii priblizhennykh konechno-raznostnykh i negladkikh variatsionnykh reshenii zadach”, Sib. zhurn. vychisl. matem., 4:1 (2001), 51–60  mathnet
    2. V. V. Smelov, “Ob obobschennom reshenii dvumernoi ellipticheskoi zadachi s kusochno-postoyannymi koeffitsientami na osnove rasschepleniya differentsialnogo operatora i ispolzovaniya spetsificheskikh bazisnykh funktsii”, Sib. zhurn. vychisl. matem., 6:1 (2003), 59–72  mathnet  zmath
    3. Smelov V., “Effective Approximation of Piecewise Smooth Functions by their Expansion Into Fast Convergent Series in Terms of Functions Formed by Eigenfunctions of Sturm-Liouville Problems”, Russ. J. Numer. Anal. Math. Model, 19:5 (2004), 449–465  crossref  mathscinet  zmath  isi  scopus
    4. V. V. Smelov, “Approximate solution of a mixed problem for a parabolic equation by means of a special basis of functions”, J. Appl. Industr. Math., 1:1 (2007), 105–115  mathnet  crossref  mathscinet
    5. Smelov V.V., “Gauss Type Quadratures Based on Trigonometric Bases”, Russ. J. Numer. Anal. Math. Model, 23:3 (2008), 265–281  crossref  mathscinet  zmath  isi  elib  scopus
    6. V. V. Smelov, “An Approximate Solution to the Integral Equations with Kernels of the Form $K(x-t)$ Which Uses a Nonstandard Basis of Trigonometric Functions”, J. Appl. Industr. Math., 4:3 (2010), 422–427  mathnet  crossref  mathscinet
    7. Smelov V.V., “Approximate Solution of Integral Equations with Kernels of the Form K(X-T) Based on a Special Basis of Trigonometric Functions”, Russ. J. Numer. Anal. Math. Model, 24:3 (2009), 297–306  crossref  mathscinet  zmath  isi  elib  scopus
    8. V. V. Smelov, A. S. Popov, “An analog to Gaussian quadrature implemented on a specific trigonometric basis”, Num. Anal. Appl., 3:4 (2010), 357–366  mathnet  crossref
    9. V. V. Smelov, “Iteratsionnyi metod poiska reshenii zadach teploprovodnosti i diffuzii chastits pri razryvnykh koeffitsientakh differentsialnogo operatora zadachi”, Sib. zhurn. industr. matem., 15:2 (2012), 128–138  mathnet  mathscinet
    10. Smelov V.V., “Construction of a Functional Basis with Automatic Fulfillment of Interface Conditions at Discontinuity Points of Coefficients of an Elliptic Operator”, Russ. J. Numer. Anal. Math. Model, 27:4 (2012), 387–398  crossref  mathscinet  zmath  isi  elib  scopus
    11. V. V. Smelov, “Osnovannye na trigonometrii bazisy i ikh preimuschestva”, Vestn. NGU. Ser. matem., mekh., inform., 13:1 (2013), 105–119  mathnet
    12. V. V. Smelov, “A network version of the non-standard trigonometric basis and its advantages with respect to a similar polynomial basis”, Num. Anal. Appl., 7:4 (2014), 336–344  mathnet  crossref  mathscinet
    13. V. V. Smelov, “Ob odnomernykh kraevykh zadachakh s razryvnymi koeffitsientami i orientirovannom na ikh reshenie spetsificheskom setochnom bazise”, Vestn. NGU. Ser. matem., mekh., inform., 14:3 (2014), 95–106  mathnet
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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