Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 01, 1997, pp. 30–36. Submitted: March 4, 1997. Published: July 31, 1997.

A LOCAL CONVERGENCE THEOREM FOR THE

INEXACT NEWTON METHOD AT SINGULAR POINTS

Ioannis K. Argyros

Abstract. If Newton’s method is used to find a solution of an equation on a Banach space, and the Fréchetderivative is singular at the solution, the convergence of Newton iterates to the solution is linear rather than quadratic. In this study we employ the inexact Newton method to restore quadratic convergence, especially in cases when Newton’s or the corrected Newton’s method cannot achieve this or cannot even be used.

1991 A.M.S. (MOS) Subject Classification Codes. 65J15, 47H17, 49D15.

Key Words and Phrases. Banach space, Newton method, singular points, quadratic convergence.

Department of Mathematics, Cameron University, Lawton, OK 73505, U.S.A. E-mail Address: ioannisa@cameron.edu \begin{matrix}c \\ ◯ \end{matrix}1997 Cameron University

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