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Convergence of Hölder Projections to Chebyshev Projections

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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.

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Funding

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).

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Authors and Affiliations

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

    V. I. Zorkal’tsev

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  1. V. I. Zorkal’tsev
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Correspondence to V. I. Zorkal’tsev.

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Translated by E. Chernokozhin

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Zorkal’tsev, V.I. Convergence of Hölder Projections to Chebyshev Projections. Comput. Math. and Math. Phys. 60, 1810–1822 (2020). https://doi.org/10.1134/S0965542520110147

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  • DOI: https://doi.org/10.1134/S0965542520110147

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