Skip to main content

Discretization of solutions to a wave equation, numerical differentiation, and function recovery with the help of computer (computing) diameter

Abstract

We study three concretizations of the notion of computer (computing) diameter, namely, the discretization of solutions to the Klein-Gordon equation, numerical differentiation, and function recovery.

This is a preview of subscription content, access via your institution.

References

  1. A. N. Kolmogorov, “Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse,” Ann. Math. (2) 37, 107–110 (1936).

    MathSciNet  MATH  Article  Google Scholar 

  2. N. Temirgaliev, “Computer (Computing) Diameter. Algebraic Number Theory and Harmonic Analysis in Recovery Problems (Quasi-Monte-Carlo Method). Theory of Embeddings and Approximation. Fourier Series,” (Special issue devoted to scientific achievements of mathematicians of L. N. Gumilev Eurasian National University, Vestn. L.N.Gumilev Evraz. Nats. Univ., 1–194 (2010)) [in Russian].

    Google Scholar 

  3. N. Temirgaliev, “Continuous and Discrete Mathematics in Organic Unity in Research Context,” Electronic edition, Inst. Of Theor. Math. and Scient. Calc. of the L.N. Gumilev Eurasian National University, Astana, 1–256 (2012)] [in Russian].

    Google Scholar 

  4. G. G. Magaril-Il’yaev and K. Yu. Osipenko, “Optimal Recovery of Functions and their Derivatives from Fourier Coefficients Prescribed with an Error,” Matem. Sborn. 193(3), 387–407 (2002).

    MathSciNet  MATH  Article  Google Scholar 

  5. A. G. Marchuk and K. Yu. Osipenko, “Best Approximation of Functions Specified with an Error at a Finite Number of Points,” Matem. Zametki 17(3), 207–212 (1975).

    MATH  Google Scholar 

  6. L. Plaskota, textitNoisy Information and Computational Complexity (Cambridge University Press, 1996).

    Book  Google Scholar 

  7. Sh. Abikenova and N. Temirgaliev, “On the Sharp Order of Informativeness of All Possible Linear Functionals in the Discretization of Solutions of the Wave Equation,” Differents. Uravneniya 46(8), 1211–1214 (2010).

    MathSciNet  MATH  Google Scholar 

  8. O. V. Lokutsievskii and M.V. Gavrikov, Foundations of Numerical Analysis (Moscow, Yanus, 1995) [in Russian].

    Google Scholar 

  9. K. I. Babenko, The Basic of Numerical Analysis (Moscow, Nauka, 1986) [in Russian].

    Google Scholar 

  10. V. S. Ryaben’kii, Introduction to Computing Mathematics (Moscow, Fizmatlit, 1994) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Temirgaliev.

Additional information

Original Russian Text © N. Temirgaliev, Sh.K. Abikenova, A.Zh. Zhubanysheva, and G.E. Taugynbaeva, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 8, pp. 86–93.

About this article

Cite this article

Temirgaliev, N., Abikenova, S.K., Zhubanysheva, A.Z. et al. Discretization of solutions to a wave equation, numerical differentiation, and function recovery with the help of computer (computing) diameter. Russ Math. 57, 75–80 (2013). https://doi.org/10.3103/S1066369X13080094

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X13080094

Keywords and phrases

  • computer (computing) diameter
  • discretization of solutions to differential equations
  • operator discretization
  • function recovery
  • informative cardinality of given set of functionals
  • limiting accuracy