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Sibirskii Zhurnal Industrial'noi Matematiki, 2023, Volume 26, Number 3, Pages 5–13
DOI: https://doi.org/10.33048/SIBJIM.2023.26.301
(Mi sjim1243)
 

This article is cited in 1 scientific paper (total in 1 paper)

A modified quadratic interpolation method for root finding

V. V. Bogdanov, Yu. S. Volkov

Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
Full-text PDF (989 kB) Citations (1)
References:
Abstract: A modification of the quadratic interpolation method for finding the root of a continuous function is proposed. Two quadratic interpolation polynomials are simultaneously constructed. It is shown that if the third derivative of the original function does not change sign on the considered interval of localization of the required root, then the root lies between the roots of the quadratic functions. This allows to significantly narrow the localization interval and reduce the number of steps to calculate the root with a given accuracy. The proposed modification of the quadratic interpolation method is used in the problem of calculating isolines when modeling the hill diagram of hydraulic turbines.
Keywords: quadratic interpolation, modeling, efficiency function of a hydraulic turbine, spline, multidimensional approximation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF–2022–0015
Received: 27.04.2023
Revised: 26.05.2023
Accepted: 07.06.2023
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 3, Pages 491–497
DOI: https://doi.org/10.1134/S1990478923030031
Document Type: Article
UDC: 519.65
Language: Russian
Citation: V. V. Bogdanov, Yu. S. Volkov, “A modified quadratic interpolation method for root finding”, Sib. Zh. Ind. Mat., 26:3 (2023), 5–13; J. Appl. Industr. Math., 17:3 (2023), 491–497
Citation in format AMSBIB
\Bibitem{BogVol23}
\by V.~V.~Bogdanov, Yu.~S.~Volkov
\paper A~modified quadratic interpolation method for~root finding
\jour Sib. Zh. Ind. Mat.
\yr 2023
\vol 26
\issue 3
\pages 5--13
\mathnet{http://mi.mathnet.ru/sjim1243}
\crossref{https://doi.org/10.33048/SIBJIM.2023.26.301}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 3
\pages 491--497
\crossref{https://doi.org/10.1134/S1990478923030031}
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  • This publication is cited in the following 1 articles:
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