Newton-like algorithms for kth root calculation
Marek Kuczma, Halina Światak (1991)
Annales Polonici Mathematici
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Displaying similar documents to “An iterative procedure for solving the Riccati equation A₂R - RA₁ = A₃ + RA₄R”
Newton-like algorithms for kth root calculation
Enclosing roots of polynomial equations and their applications to iterative processes.
Argyros, I.K., Hilout, S. (2009)
Surveys in Mathematics and its Applications
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Convergence of Newton-Like-Iterative Methods.
T.J. Ypma (1984)
Numerische Mathematik
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Error Bounds of Newton Type Process on Banach Spaces.
H.C. Lai, P.Y. Wu (1982)
Numerische Mathematik
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A method for obtaining third-order iterative formulas.
Herceg, Djordje, Herceg, Dragoslav (2008)
Novi Sad Journal of Mathematics
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Extending the applicability of Newton's method using nondiscrete induction
Ioannis K. Argyros, Saïd Hilout (2013)
Czechoslovak Mathematical Journal
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We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra,...
Nondiscrete induction and an inversion-free modification of Newton's method
Florian-Alexandru Potra, Vlastimil Pták (1983)
Časopis pro pěstování matematiky
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An iterative method for computing zeros of operators satisfying autonomous differential equations.
Argyros, Ioannis K. (2004)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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A new approach for finding weaker conditions for the convergence of Newton's method
Ioannis K. Argyros (2005)
Applicationes Mathematicae
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The Newton-Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton's method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cost. Moreover, finer error bounds and at least as precise information on the location of the...
A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence
Kyurkchiev, Nikolay, Iliev, Anton (2009)
Serdica Journal of Computing
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This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv. In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence. ...