Loading [MathJax]/jax/output/SVG/config.js
Sibirskii Zhurnal Vychislitel'noi Matematiki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sib. Zh. Vychisl. Mat.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sibirskii Zhurnal Vychislitel'noi Matematiki, 2005, Volume 8, Number 1, Pages 77–88 (Mi sjvm211)  
This article is cited in 16 scientific papers (total in 16 papers)

Approximation by local parabolic splines with arbitrary knots

V. T. Shevaldin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (223 kB) Citations (16)
References:
PDF
HTML
Abstract: For the class of the functions $W_{\infty}^2$ with almost bounded second derivatives, a new linear local method of parabolic spline approximation on an arbitrary grid is constructed. This method has some smoothing properties and inherits the monotonicity and the convexity of the initial data (values of a function at the grid points). On this class the error of approximation by the splines constructed is exactly calculated.
Key words: local method, parabolic spline approximation, the error of approximation.
Received: 26.04.2004
Bibliographic databases:
UDC: 519.65
Language: Russian
Citation: V. T. Shevaldin, “Approximation by local parabolic splines with arbitrary knots”, Sib. Zh. Vychisl. Mat., 8:1 (2005), 77–88
Citation in format AMSBIB
\Bibitem{She05}
\by V.~T.~Shevaldin
\paper Approximation by local parabolic splines with arbitrary knots
\jour Sib. Zh. Vychisl. Mat.
\yr 2005
\vol 8
\issue 1
\pages 77--88
\mathnet{http://mi.mathnet.ru/sjvm211}
\zmath{https://zbmath.org/?q=an:1075.41008}
Linking options:
  • https://www.mathnet.ru/eng/sjvm211
  • https://www.mathnet.ru/eng/sjvm/v8/i1/p77
    • This publication is cited in the following 16 articles:
    1. Varun, Mathur N., Bahadur S., Mathur P., “Approximation of Non-Interpolatory Complex Parabolic Spline on the Unit Circle”, Filomat, 35:10 (2021), 3549–3556  crossref  mathscinet  isi  scopus
    2. V. T. Shevaldin, “Local approximation by parabolic splines in the mean with large averaging intervals”, Math. Notes, 108:5 (2020), 733–742  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Yu. S. Volkov, V. V. Bogdanov, “On error estimates of local approximation by splines”, Siberian Math. J., 61:5 (2020), 795–802  mathnet  crossref  crossref  isi  elib
    4. Yu. N. Subbotin, V. T. Shevaldin, “A Method for the Construction of Local Parabolic Splines with Additional Knots”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S151–S166  mathnet  crossref  crossref  isi  elib
    5. 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
    6. E. V. Strelkova, V. T. Shevaldin, “On Lebesgue constants of local parabolic splines”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 192–198  mathnet  crossref  mathscinet  isi  elib
    7. E. V. Strelkova, V. T. Shevaldin, “Local exponential splines with arbitrary knots”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 189–194  mathnet  crossref  mathscinet  isi  elib
    8. Lytvyn O.N., Iarmosh E.V., “Some Aspects of Modeling for Management in the Process of Forming a Students' Number in Higher Educational Institutions as the Actual Economic Educational Problem”, J. Automat. Inf. Sci., 45:7 (2013), 30–40  crossref  isi  elib  scopus
    9. Yu. S. Volkov, E. G. Pytkeev, V. T. Shevaldin, “Orders of approximation by local exponential splines”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 175–184  mathnet  crossref  isi  elib
    10. Yu. S. Volkov, V. T. Shevaldin, “Usloviya formosokhraneniya pri interpolyatsii splainami vtoroi stepeni po Subbotinu i po Marsdenu”, Tr. IMM UrO RAN, 18, no. 4, 2012, 145–152  mathnet  elib
    11. Yu. S. Volkov, E. V. Strelkova, V. T. Shevaldin, “Local approximation by splines with displacement of nodes”, Siberian Adv. Math., 23:1 (2013), 69–75  mathnet  crossref  mathscinet  elib
    12. Kobylkin K.S., “Primenenie formosokhranyayuschikh splainov dlya otsenki plotnosti raspredeleniya zemli mezhdu krestyanskimi khozyaistvami posle reformy 1863 goda”, Vestn. Uralskogo in-ta ekonomiki, upravleniya i prava, 2010, no. 3, 94–99  elib
    13. Yu. N. Subbotin, “Form-preserving exponential approximation”, Russian Math. (Iz. VUZ), 53:11 (2009), 46–52  mathnet  crossref  mathscinet  zmath
    14. 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
    15. 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
    16. E. V. Shevaldina, “Approksimatsiya lokalnymi eksponentsialnymi splainami s proizvolnymi uzlami”, Sib. zhurn. vychisl. matem., 9:4 (2006), 391–402  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
    Statistics & downloads:
    Abstract page:1147
    Full-text PDF :336
    References:115
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025