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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/znsl783
https://www.mathnet.ru/eng/znsl/v312/p256
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