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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 11, Pages 1867–1880 (Mi zvmmf11158)  

Optimal control

Convergence of Hölder projections to chebyshev projections

V. I. Zorkal'tsev

Limnological Institute, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033 Russia

Abstract: The problem of finding a point of a linear manifold with a minimal weighted Chebyshev norm is considered. In particular, to such a problem, the Chebyshev approximation is reduced. An algorithm that always produces a unique solution to this problem is presented. The algorithm consists in finding relatively internal points of optimal solutions of a finite sequence of linear programming problems. It is proved that the solution generated by this algorithm is the limit to which the Hölder projections of the origin of coordinates onto a linear manifold converge with infinitely increasing power index of the Hölder norms using the same weight coefficients as the Chebyshev norm.

Key words: Hölder norms, Chebyshev norms, Hölder projections, Chebyshev projections, Chebyshev approximation, Haar condition, relatively interior points of optimal solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-07-00322
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0279-2019-0003
This work was supported by the Russian Foundation for Basic Research (project no. 19-07-00322) and the Russian Academy of Sciences (project no. 0279-2019-0003).


DOI: https://doi.org/10.31857/S0044466920110150


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:11, 1810–1822

Bibliographic databases:

UDC: 519.6
Received: 30.01.2020
Revised: 07.02.2020
Accepted:07.07.2020

Citation: V. I. Zorkal'tsev, “Convergence of Hölder projections to chebyshev projections”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1867–1880; Comput. Math. Math. Phys., 60:11 (2020), 1810–1822

Citation in format AMSBIB
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\by V.~I.~Zorkal'tsev
\paper Convergence of H\"older projections to chebyshev projections
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 11
\pages 1867--1880
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\crossref{https://doi.org/10.31857/S0044466920110150}
\elib{https://elibrary.ru/item.asp?id=44038905}
\transl
\jour Comput. Math. Math. Phys.
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\vol 60
\issue 11
\pages 1810--1822
\crossref{https://doi.org/10.1134/S0965542520110147}
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