AN ERROR ANALYSIS OF STIRLING'S METHOD IN BANACH SPACES

Authors

  • IOANNIS K. ARGYROS Cameron University, Department of Mathematics, Lawton, OK 73505-6377, U. S. A.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4481

Keywords:

Stirling's method, nondiscrete mathematical induction, Banach space

Abstract

The method of nondiscrete mathematical induction is applied to Stirling's method. The method yields a very simple proof of the convergence and error estimates which are generally better than those given in the literature.

References

I. K. Argyros, "On Newton's method and nondiscrete mathematical induction." Bulll. Austral. Math. Soc., Vol. 38 (1988), 131-140.

L. V. Kantorovich, ''Functional analysis and applied mathematics." Uspekhi Mat. Nauk. 3, (1948), 89-185.

J. M . Ortega and W. C. Rheiuboldt, "Iterative solution of nonlinear equations in several variables." New York, Academic Press, 1970.

F. A. Potra and V. Ptak, "Sharp error bounds for Newton's process." Numer. Math. 34, (1980), 63-72.

----, "Nondiscrete induction and iterative processes." Pitman Publ. Boston, 1984.

L. B. Rall, "Computational solution of nonlinear operator equations." John Wiley Publ. 1969.

----, "Convergence of Stirling's method in Banach spaces." Aeq. Math., Vol. 12, (1975), 12-19.

J. Stirling, "Methods differentials: sivc tractatus de surnmatione et interpolatione se- rierum infinitarum." W. Boyer, London, 1730.

R. A. Tapia, "The Kantorovich theorem for Newton's method", Amer. Math. Soc. Montidy 78, (1971), 389-392.

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Published

1993-06-01

How to Cite

ARGYROS, I. K. (1993). AN ERROR ANALYSIS OF STIRLING’S METHOD IN BANACH SPACES. Tamkang Journal of Mathematics, 24(2), 115-133. https://doi.org/10.5556/j.tkjm.24.1993.4481

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