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 Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 11, Pages 1819–1829 (Mi zvmmf217)

On certain two-sided analogues of Newton's method for solving nonlinear eigenvalue problems

B. M. Podlevskii

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. Nauchnaya 3-b, Lviv, 79000, Ukraine

Abstract: Iterative algorithms for finding two-sided approximations to the eigenvalues of nonlinear algebraic eigenvalue problems are examined. These algorithms use an efficient numerical procedure for calculating the first and second derivatives of the determinant of the problem. Computational aspects of this procedure as applied to finding all the eigenvalues from a given complex-plane domain in a nonlinear eigenvalue problem are analyzed. The efficiency of the algorithms is demonstrated using some model problems.

Key words: nonlinear algebraic eigenvalue problems, iterative algorithm, two-sided analogue of Newton's method.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:11, 1745–1755

Bibliographic databases:

UDC: 519.614
Revised: 01.06.2007

Citation: B. M. Podlevskii, “On certain two-sided analogues of Newton's method for solving nonlinear eigenvalue problems”, Zh. Vychisl. Mat. Mat. Fiz., 47:11 (2007), 1819–1829; Comput. Math. Math. Phys., 47:11 (2007), 1745–1755

Citation in format AMSBIB
\Bibitem{Pod07} \by B.~M.~Podlevskii \paper On certain two-sided analogues of Newton's method for solving nonlinear eigenvalue problems \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2007 \vol 47 \issue 11 \pages 1819--1829 \mathnet{http://mi.mathnet.ru/zvmmf217} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2405027} \transl \jour Comput. Math. Math. Phys. \yr 2007 \vol 47 \issue 11 \pages 1745--1755 \crossref{https://doi.org/10.1134/S0965542507110024} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36448953130} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Podlevskyi B.M., “Numerical Algorithms of Finding the Branching Lines and Biffurcation Points of Solutions of Nonlinear Integral Equation Arising in the Theory of Antennas Synthesis”, Diped-2009: 2009 International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, Proceedings, 2009, 197–203
2. B. M. Podlevskii, “O nekotorykh nelineinykh dvukhparametricheskikh spektralnykh zadachakh matematicheskoi fiziki”, Matem. modelirovanie, 22:5 (2010), 131–145
3. Zhanlav T., Chuluunbaatar O., Ulziibayar V., “Two-Sided Approximation for Some Newton's Type Methods”, Appl. Math. Comput., 236 (2014), 239–246
4. T. Zhanlav, O. Chuluunbaatar, V. Ulziibayar, “A brief description of two-sided approximation for some Newton’s type methods”, Matem. modelirovanie, 26:11 (2014), 71–77
5. Podlevskyi B.M., “Determination the Quantity of Eigenvalue For Two-Parameter Eigenvalue Problems in the Prescribed Region”, J. Numer. Appl. Math., 3:126 (2017), 104–109
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