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Mat. Zametki, 2005, Volume 77, Issue 3, Pages 354–363 (Mi mz2498)  

This article is cited in 8 scientific papers (total in 8 papers)

Approximation by local trigonometric splines

K. V. Kostousova, V. T. Shevaldinb

a Ural State University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: For the class $W_\infty^{\mathscr L_2}=\{f:f'\in AC, \|f"+\alpha^2f\|_\infty\leqslant1\}$ of 1-periodic functions, we use the linear noninterpolating method of trigonometric spline approximation possessing extremal and smoothing properties and locally inheriting the monotonicity of the initial data, i.e., the values of a function from $W_\infty^{\mathscr L_2}$ at the points of a uniform grid. The approximation error is calculated exactly for this class of functions in the uniform metric. It coincides with the Kolmogorov and Konovalov widths.

DOI: https://doi.org/10.4213/mzm2498

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English version:
Mathematical Notes, 2005, 77:3, 326–334

Bibliographic databases:

UDC: 519.65
Received: 01.07.2003

Citation: K. V. Kostousov, V. T. Shevaldin, “Approximation by local trigonometric splines”, Mat. Zametki, 77:3 (2005), 354–363; Math. Notes, 77:3 (2005), 326–334

Citation in format AMSBIB
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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. V. T. Shevaldin, “Approximation by local $L$-splines corresponding to a linear differential operator of the second order”, Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S178–S197  mathnet  crossref  mathscinet  zmath  elib
    2. E. V. Shevaldina, “Approksimatsiya lokalnymi eksponentsialnymi splainami s proizvolnymi uzlami”, Sib. zhurn. vychisl. matem., 9:4 (2006), 391–402  mathnet
    3. Yu. N. Subbotin, “Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S231–S242  mathnet  crossref  elib
    4. Yu. N. Subbotin, “Form-preserving exponential approximation”, Russian Math. (Iz. VUZ), 53:11 (2009), 46–52  mathnet  crossref  mathscinet  zmath
    5. Xiao W., “Relative widths of function classes of L (2)(T) defined by a linear differential operator in L (q) (T)”, Anal Math, 37:1 (2011), 65–81  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. E. V. Strelkova, V. T. Shevaldin, “O ravnomernykh konstantakh Lebega lokalnykh trigonometricheskikh splainov tretego poryadka”, Tr. IMM UrO RAN, 22, no. 2, 2016, 245–254  mathnet  crossref  mathscinet  elib
    7. V. T. Shevaldin, “Uniform Lebesgue constants of local spline approximation”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 196–202  mathnet  crossref  crossref  isi  elib
    8. V. T. Shevaldin, “On integral Lebesgue constants of local splines with uniform knots”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S158–S165  mathnet  crossref  crossref  isi  elib
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