RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 1, Pages 105–114 (Mi mz9853)

On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables

M. B. A. Babaev

Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR

Abstract: We present a simple method for finding the values of the best approximation of a function of $n$ variables of a given class by means of sums of two functions of a fewer number of variables; we establish close upper and lower bounds for the value of the best approximation to the function $f(x_1,…,x_n)$, having the mixed derivative $f_{x_1…x_n}$, by means of sums of a function of $n-1$ variables.

Full text: PDF file (991 kB)

English version:
Mathematical Notes, 1972, 12:1, 495–500

Bibliographic databases:

UDC: 517.5

Citation: M. B. A. Babaev, “On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables”, Mat. Zametki, 12:1 (1972), 105–114; Math. Notes, 12:1 (1972), 495–500

Citation in format AMSBIB
\Bibitem{Bab72} \by M.~B.~A.~Babaev \paper On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables \jour Mat. Zametki \yr 1972 \vol 12 \issue 1 \pages 105--114 \mathnet{http://mi.mathnet.ru/mz9853} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=326243} \zmath{https://zbmath.org/?q=an:0237.41010} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 1 \pages 495--500 \crossref{https://doi.org/10.1007/BF01094399} 

• http://mi.mathnet.ru/eng/mz9853
• http://mi.mathnet.ru/eng/mz/v12/i1/p105

 SHARE:

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. È. Ismailov, “Methods for computing the least deviation from the sums of functions of one variable”, Siberian Math. J., 47:5 (2006), 883–888
2. V. E. Ismailov, “Approximation by sums of ridge functions with fixed directions”, St. Petersburg Math. J., 28:6 (2017), 741–772
3. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169
•  Number of views: This page: 116 Full text: 57 First page: 1