Chebyshevskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Chebyshevskii Sb., 2018, Volume 19, Issue 3, Pages 241–256 (Mi cheb692)  

This article is cited in 3 scientific papers (total in 3 papers)

Approximation of quadratic algebraic lattices and nets by integer lattices and rational nets

A. V. Mikhlyaeva

Orenburg State University

Abstract: This paper is devoted to the approximation of quadratic algebraic lattices and grids by integer lattices and rational grids.
A General formulation of the problem of approximation of algebraic lattices and corresponding meshes by integer lattices and rational meshes is given.
In the case of a simple $p$ of the form $p=4k+3$ or $p=2$, we consider an integer lattice given $m$by a suitable fraction to the number $\sqrt{p}$. The corresponding algebraic lattice and the generalized parallelepipedal grid are written out explicitly.
To determine the quality of the corresponding generalized parallelepipedal grid, a quality function is defined, which requires $O(N)$ arithmetic operations for its calculation, where $N$ — is the number of grid points. The Central result is an algorithm for computing a quality function for $O(\sqrt{N})$ arithmetic operations.
We hypothesize the existence of an algorithm that requires $O(\ln{N})$ arithmetic operations. An approach for calculating sums with integral parts of linear functions is outlined.

Keywords: quadratic fields, approximation of algebraic grids, quality function, generalized parallelepipedal grid.

DOI: https://doi.org/10.22405/2226-8383-2018-19-3-241-256

Full text: PDF file (661 kB)
References: PDF file   HTML file

UDC: 511.9
Received: 28.08.2018
Accepted:15.10.2018

Citation: A. V. Mikhlyaeva, “Approximation of quadratic algebraic lattices and nets by integer lattices and rational nets”, Chebyshevskii Sb., 19:3 (2018), 241–256

Citation in format AMSBIB
\Bibitem{Mik18}
\by A.~V.~Mikhlyaeva
\paper Approximation of quadratic algebraic lattices and nets by integer lattices and rational nets
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 3
\pages 241--256
\mathnet{http://mi.mathnet.ru/cheb692}
\crossref{https://doi.org/10.22405/2226-8383-2018-19-3-241-256}
\elib{https://elibrary.ru/item.asp?id=39454401}


Linking options:
  • http://mi.mathnet.ru/eng/cheb692
  • http://mi.mathnet.ru/eng/cheb/v19/i3/p241

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. N. Kormacheva, “O nepolnykh chastnykh odnoi tsepnoi drobi”, Chebyshevskii sb., 20:1 (2019), 298–306  mathnet  crossref
    2. A. V. Mikhlyaeva, “Funktsiya kachestva dlya priblizheniya kvadratichnykh algebraicheskikh setok”, Chebyshevskii sb., 20:1 (2019), 307–312  mathnet  crossref
    3. A. N. Kormacheva, “Priblizhenie kvadratichnykh algebraicheskikh reshetok tselochislennymi reshetkami”, Chebyshevskii sb., 20:2 (2019), 366–373  mathnet  crossref
  • Number of views:
    This page:73
    Full text:14
    References:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022