Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1997, pp. 43–47. Submitted: November 10, 1997. Published: December 30, 1997.

APPLICATIONS OF A SPECIAL REPRESENTATION OF ANALYTIC FUNCTIONS

I.K. Argyros, L.F. Mahrt, and F. Szidarovszky

Abstract. A special factored representation of analytic functions is applied to obtain iteration methods for solving nonlinear equations. As particular examples, the Newton method, and the Halley method are derived.

1991 A.M.S. (MOS) Subject Classification Codes. 26C15, 65, 47, 49.

Key Words and Phrases. Rational function, partial decomposition, fast algorithm, Newton’s method.

Department of Mathematics, Cameron University, Lawton, OK 73505, U.S.A. E-mail Address: ioannisa@cameron.edu Systems and Industrial Engineering Department, University of Arizona, Tucson, Az 85721, U.S.A. E-mail address: lfmahrt@ccgate.hac.com E-mail address: szidar@sie.arizona.edu \begin{matrix}c \\ ◯ \end{matrix}1997 Cameron University

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