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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 312, Pages 256–274 (Mi znsl783)  
This article is cited in 23 scientific papers (total in 23 papers)

Newton–Kantorovich method and its global convergence

B. T. Polyak

Institute of Control Sciences, Russian Academy of Sciences
Full-text PDF (299 kB) Citations (23)
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Abstract: In 1948, L. V. Kantorovich extended the Newton method for solving nonlinear equations to functional spaces. This event cannot be overestimated: the Newton–Kantorovich method became a powerful tool in numerical analysis as well as in pure mathematics. We address basic ideas of the method in the historical perspective and focus on some recent applications and extensions of the method and some approaches to overcoming its local nature.
Received: 28.07.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 133, Issue 4, Pages 1513–1523
DOI: https://doi.org/10.1007/s10958-006-0066-1
Bibliographic databases:
UDC: 519.62
Language: English
Citation: B. T. Polyak, “Newton–Kantorovich method and its global convergence”, Representation theory, dynamical systems. Part XI, Special issue, Zap. Nauchn. Sem. POMI, 312, POMI, St. Petersburg, 2004, 256–274; J. Math. Sci. (N. Y.), 133:4 (2006), 1513–1523
Citation in format AMSBIB
\Bibitem{Pol04}
\by B.~T.~Polyak
\paper Newton--Kantorovich method and its global convergence
\inbook Representation theory, dynamical systems. Part~XI
\bookinfo Special issue
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 312
\pages 256--274
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl783}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2117893}
\zmath{https://zbmath.org/?q=an:1080.65534}
\elib{https://elibrary.ru/item.asp?id=9129091}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 133
\issue 4
\pages 1513--1523
\crossref{https://doi.org/10.1007/s10958-006-0066-1}
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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