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Mat. Zametki, 1998, Volume 63, Issue 4, Pages 562–571 (Mi mz1316)  

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

Asymptotic error estimates for the method of simple iteration and for the modified and generalized Newton methods

G. Yu. Kulikov

Ulyanovsk State University

Abstract: We find asymptotic error estimates for the method of simple iteration and for the modified and generalized Newton methods. The results, in contrast with the classical ones, provide explicit error estimates for these iterative processes in terms of their parameters, and this plays a decisive role not only for the proof of the convergence of combined methods, but also for determining the order of convergence. Moreover, in practice this allows us to theoretically evaluate the number of iterations sufficient for constructing the combined method of maximal order, and therefore to find the optimal number of iterations.

DOI: https://doi.org/10.4213/mzm1316

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English version:
Mathematical Notes, 1998, 63:4, 494–502

Bibliographic databases:

UDC: 519.615.5
Received: 11.11.1996
Revised: 28.10.1997

Citation: G. Yu. Kulikov, “Asymptotic error estimates for the method of simple iteration and for the modified and generalized Newton methods”, Mat. Zametki, 63:4 (1998), 562–571; Math. Notes, 63:4 (1998), 494–502

Citation in format AMSBIB
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\by G.~Yu.~Kulikov
\paper Asymptotic error estimates for the method of simple iteration and for the modified and generalized Newton methods
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\yr 1998
\vol 63
\issue 4
\pages 562--571
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\zmath{https://zbmath.org/?q=an:0922.65043}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 4
\pages 494--502
\crossref{https://doi.org/10.1007/BF02311252}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075783100031}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. Yu. Kulikov, “On using Newton-type iterative methods for solving systems of differential-algebraic equations of index 1”, Comput. Math. Math. Phys., 41:8 (2001), 1122–1131  mathnet  mathscinet  zmath
    2. Kulikov, GY, “On implicit extrapolation methods for ordinary differential equations”, Russian Journal of Numerical Analysis and Mathematical Modelling, 17:1 (2002), 41  crossref  mathscinet  isi  scopus
    3. Kulikov, GY, “One-step methods and implicit extrapolation technique for index 1 differential-algebraic systems”, Russian Journal of Numerical Analysis and Mathematical Modelling, 19:6 (2004), 527  crossref  mathscinet  zmath  isi
    4. Kulikov, GY, “Asymptotic error estimate of iterative Newton-type methods and its practical application”, Computational Science and Its Applications - Iccsa 2004, Pt 3, 3045 (2004), 667  crossref  mathscinet  zmath  isi
    5. Kullkov, GY, “Asymptotic error estimate for general Newton-type methods and its application to differential equations”, Russian Journal of Numerical Analysis and Mathematical Modelling, 22:6 (2007), 567  crossref  mathscinet  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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