Abstract:
The properties of polynomials Rn+5(x), the least deviating from zero in L[−1,1] metric with five given leading coefficients, whose forms were calculated earlier, are studied. Theorems 1, 2 with Theorem A contain a final classification of polynomials Rn+5(x), whose number of sign changes in (−1,1) is exactly equal to (n+1).
Key words:
non-negative, non-positive polynomials, polynomials, the least deviating from zero in integral metric.
Citation:
V. È. Gheit, V. V. Gheit, “On polynomials, the least deviating from zero in L[−1,1] metric, with five prescribed coefficients”, Sib. Zh. Vychisl. Mat., 12:1 (2009), 29–40; Num. Anal. Appl., 2:1 (2009), 24–33
\Bibitem{GheGhe09}
\by V.~\`E.~Gheit, V.~V.~Gheit
\paper On polynomials, the least deviating from zero in~$L[-1,1]$ metric, with five prescribed coefficients
\jour Sib. Zh. Vychisl. Mat.
\yr 2009
\vol 12
\issue 1
\pages 29--40
\mathnet{http://mi.mathnet.ru/sjvm3}
\transl
\jour Num. Anal. Appl.
\yr 2009
\vol 2
\issue 1
\pages 24--33
\crossref{https://doi.org/10.1134/S1995423909010030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65249185603}
Linking options:
https://www.mathnet.ru/eng/sjvm3
https://www.mathnet.ru/eng/sjvm/v12/i1/p29
This publication is cited in the following 2 articles:
Ioannis Stamatopoulos, Ioannis Koutzoglou, Dimitrios I. Karatzidis, Zaharias D. Zaharis, Pavlos I. Lazaridis, Nikolaos V. Kantartzis, “Efficient Filter Design to Compensate Fabrication Imperfections in 6G Communication Systems”, Sensors, 23:24 (2023), 9825
Arestov V., Deikalova M., “Nikol'Skii Inequality Between the Uniform Norm and l (Q) -Norm With Jacobi Weight of Algebraic Polynomials on An Interval”, Anal. Math., 42:2 (2016), 91–120
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