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 Chebyshevskii Sb., 2020, Volume 21, Issue 3, Pages 223–231 (Mi cheb937)

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Quality function for the approximation of quadratic algebraic nets — II

A. V. Mikhlyaeva

Orenburg State University (Orenburg)

Abstract: This paper is devoted to the construction of fast algorithms for calculating the quality function of rational grids that approximate quadratic algebraic grids in the General case of the maximum lattice of integer algebraic numbers.
It is shown that the generalized parallelepipedal net approximating the quadratic algebraic net is parallelepiped.As a consequence, an algorithm for calculating the quality function for $O(\ln{N})$ arithmetic operations is constructed.

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

 Funding Agency Grant Number Russian Foundation for Basic Research 19-41-710004_ð_à The reported study was funded by RFBR, project number 19-41-710004_r_a.

DOI: https://doi.org/10.22405/2226-8383-2018-21-3-223-231

Full text: PDF file (681 kB)

UDC: 511.9
Accepted:22.10.2020

Citation: A. V. Mikhlyaeva, “Quality function for the approximation of quadratic algebraic nets — II”, Chebyshevskii Sb., 21:3 (2020), 223–231

Citation in format AMSBIB
\Bibitem{Mik20} \by A.~V.~Mikhlyaeva \paper Quality function for the approximation of quadratic algebraic nets~---~II \jour Chebyshevskii Sb. \yr 2020 \vol 21 \issue 3 \pages 223--231 \mathnet{http://mi.mathnet.ru/cheb937} \crossref{https://doi.org/10.22405/2226-8383-2018-21-3-223-231}