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2000 | 27 | 3 | 369-375
Tytuł artykułu

The effect of rounding errors on a certain class of iterative methods

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Języki publikacji
EN
Abstrakty
EN
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.
Rocznik
Tom
27
Numer
3
Strony
369-375
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-22
Twórcy
  • Cameron University, Department of Mathematics, Lawton, OK 73505, U.S.A.
Bibliografia
  • [1] I. K. Argyros, On the convergence of some projection methods with perturbations, J. Comput. Appl. Math. 36 (1991), 255-258.
  • [2] I. K. Argyros, Concerning the radius of convergence of Newton's method and applications, Korean J. Comput. Appl. Math. 6 (1999), 451-462.
  • [3] I. K. Argyros and F. Szidarovszky, The Theory and Application of Iteration Methods, CRC Press, Boca Raton, FL, 1993.
  • [4] R. S. Dembo, S. C. Eisenstat and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal. 19 (1982), 400-408.
  • [5] L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
  • [6] T. J. Ypma, Numerical solution of systems of nonlinear algebraic equations, Ph.D. thesis, Oxford, 1982.
  • [7] T. J. Ypma, Affine invariant convergence results for Newton's method, BIT 22 (1982), 108-118.
  • [8] T. J. Ypma, The effect of rounding errors on Newton-like methods, IMA J. Numer. Anal. 3 (1983), 109-118.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-zmv27i3p369bwm
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