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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 7, Pages 1181–1186 (Mi zvmmf4558)  
This article is cited in 3 scientific papers (total in 3 papers)

Determining the multiplicity of a root of a nonlinear algebraic equation

N. N. Kalitkina, I. P. Poshivaylob

a Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
b Moscow State Institute of Electronic Engineering (Technical University), Zelenograd, Moscow, 124498, Russia
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Abstract: Newton's method is most frequently used to find the roots of a nonlinear algebraic equation. The convergence domain of Newton's method can be expanded by applying a generalization known as the continuous analogue of Newton's method. For the classical and generalized Newton methods, an effective root-finding technique is proposed that simultaneously determines root multiplicity. Roots of high multiplicity (up to 10) can be calculated with a small error. The technique is illustrated using numerical examples.
Key words: nonlinear algebraic equation, numerical root finding, root multiplicity determination, generalized Newton method.
Received: 30.03.2007
Revised: 29.01.2008
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 7, Pages 1113–1118
DOI: https://doi.org/10.1134/S096554250807004X
Bibliographic databases:
Document Type: Article
UDC: 519.615.5
Language: Russian
Citation: N. N. Kalitkin, I. P. Poshivaylo, “Determining the multiplicity of a root of a nonlinear algebraic equation”, Zh. Vychisl. Mat. Mat. Fiz., 48:7 (2008), 1181–1186; Comput. Math. Math. Phys., 48:7 (2008), 1113–1118
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/zvmmf4558
  • https://www.mathnet.ru/eng/zvmmf/v48/i7/p1181
    • This publication is cited in the following 3 articles:
    1. F. Soleymani, D.K.R. Babajee, “Computing multiple zeros using a class of quartically convergent methods”, Alexandria Engineering Journal, 52:3 (2013), 531  crossref
    2. N. N. Kalitkin, L. V. Kuzmina, “Pretsizionnoe vychislenie kratnykh kornei metodom sekuschikh s ekstrapolyatsiei”, Matem. modelirovanie, 23:6 (2011), 33–58  mathnet  mathscinet
    3. N. N. Kalitkin, L. V. Kuzmina, “Calculation of roots and there multiplicity for nonlinear equation”, Math. Models Comput. Simul., 3:1 (2011), 65–80  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:97
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