Abstract:
The paper considers a multivariate analogue of the Chebyshev problem on the cube
concerning the construction of polynomials of least deviation from zero.
A classification of monomials possessing a unique
polynomial of best approximation in the space of continuous
functions on the unit cube in Rn is given. Precise solutions
in some weighted spaces Lp are found.
\Bibitem{Yud08}
\by V.~A.~Yudin
\paper Best approximation to monomials on a~cube
\jour Sb. Math.
\yr 2008
\vol 199
\issue 8
\pages 1251--1262
\mathnet{http://mi.mathnet.ru/eng/sm4089}
\crossref{https://doi.org/10.1070/SM2008v199n08ABEH003961}
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Linking options:
https://www.mathnet.ru/eng/sm4089
https://doi.org/10.1070/SM2008v199n08ABEH003961
https://www.mathnet.ru/eng/sm/v199/i8/p149
This publication is cited in the following 2 articles:
M. Dressler, S. Foucart, M. Joldes, E. de Klerk, J.B. Lasserre, Y. Xu, “Optimization-aided construction of multivariate Chebyshev polynomials”, Journal of Approximation Theory, 2024, 106116
V. A. Yudin, “Polynomials of least deviation from zero”, Proc. Steklov Inst. Math., 280 (2013), 292–295
Citation in format AMSBIB
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