Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. POMI, 2004, Volume 312, Pages 256–274 (Mi znsl783)  

This article is cited in 5 scientific papers (total in 5 papers)

Newton–Kantorovich method and its global convergence

B. T. Polyak

Institute of Control Sciences, Russian Academy of Sciences

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.

Full text: PDF file (299 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2006, 133:4, 1513–1523

Bibliographic databases:

UDC: 519.62
Received: 28.07.2004
Language:

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://www.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:
  • http://mi.mathnet.ru/eng/znsl783
  • http://mi.mathnet.ru/eng/znsl/v312/p256

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Murtola T., Karttunen M., Vattulainen I., “Systematic coarse graining from structure using internal states: Application to phospholipid/cholesterol bilayer”, J. Chem. Phys., 131:5 (2009), 055101, 15 pp.  crossref  adsnasa  isi  elib  scopus
    2. Anitescu M., “Spectral finite-element methods for parametric constrained optimization problems”, SIAM J. Numer. Anal., 47:3 (2009), 1739–1759  crossref  mathscinet  zmath  isi  elib  scopus
    3. Peris R., Marquina A., Candela V., “The convergence of the perturbed Newton method and its application for ill-conditioned problems”, Applied Mathematics and Computation, 218:7 (2011), 2988–3001  crossref  mathscinet  zmath  isi  scopus
    4. Boikov I.V., “On a Continuous Method for Solving Nonlinear Operator Equations”, Differ. Equ., 48:9 (2012), 1288–1295  crossref  mathscinet  zmath  isi  elib  scopus
    5. Fernandez J., Veron M., “Newton'S Method: An Updated Approach of Kantorovich'S Theory”, Newton'S Method: An Updated Approach of Kantorovich'S Theory, Frontiers in Mathematics, Birkhauser Verlag Ag, 2017, 1–166  crossref  mathscinet  isi
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:587
    Full text:258
    References:66

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021