Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE EFFECT OF ROUNDING ERRORS ON NEWTON METHODS

  • Published : 2000.09.01

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Abstract

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 second Frechet-derivative 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.

Keywords

References

  1. J. Comput. Appl. Math. v.36 On the convergence of some projection methods with perturbations I. K. argyros
  2. J. Comp. Appl. Math. v.6 no.3 Concerning the radius of convergence of Newton's method and applications I. K. Argyros
  3. The Theory and Application of Iteration Methods I. K. Argyros;F. Szidarovszky
  4. SIAM J. Numer. Anal. v.19 Inexact Newton methods R. S. Dembo;S. C. Eisenstat;T. Steihaug
  5. Functional Analysis L. V. Kantorovich;G. P. Akilov
  6. Ph.D. Thesis, Oxford Numerial solution of systems of nonlinear algebraic equations T. J. Ypma
  7. BIT v.22 Affine invariant convergence results for Newton's method T. J. Ypma
  8. IMA J. Num. Anal. v.3 The effect of rounding errors on Newton-like methods T. J. Ypma