MAJORIZING SEQUENCES FOR NEWTON'S METHOD

Authors

  • J. M. GUTIERREZ University of La Rioja, Dpt. Mathematics and Computation., C/Luis de Ulloa S/N, 26004, Logrono, Spain.
  • M. A. HERNANDEZ University of La Rioja, Dpt. Mathematics and Computation., C/Luis de Ulloa S/N, 26004, Logrono, Spain.

DOI:

https://doi.org/10.5556/j.tkjm.29.1998.4270

Keywords:

Nonlinear equations in Banach spaces,, Newt9n's method, majorizing sequences

Abstract

Majorizing sequences for Newton's method are analysed from a new standpoint. As a consequence, we give convergence results under assumptions different from the classical Kantorovich conditions.

References

L. V. Kantorovich and G. P. Akilov, "Functional Analysis," Pergamon Press, Oxford, 1982.

W. C. Rheinholdt, "A unified convergence theory for a class of iterative process," SIAM J. Numer. Anal., 5(1968), 42-63.

L. B. Rall, "Computational solution of nonlinear operator equations," Robert E. Krieger Publishing Company, Inc., New York, 1979.

J. M. Gutierrez, M. A. Hernandez and M. A. Salanova, "Accesibility of solutions by New­ton's method," Inter. J. Computer Math., 57(1995), 239-247.

A. M. Ostrowski, "Solution of equations and systems of equations," Academic Press, New York, 1973.

J. F. Traub, "Iterative methods for solution of equations," Prentice-Hall, New Jersey, 1964.

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Published

1998-09-01

How to Cite

GUTIERREZ, J. M., & HERNANDEZ, M. A. (1998). MAJORIZING SEQUENCES FOR NEWTON’S METHOD. Tamkang Journal of Mathematics, 29(3), 199-202. https://doi.org/10.5556/j.tkjm.29.1998.4270

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Papers