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Steffensen type methods for solving non-linear equations. (English) Zbl 1193.65063
Summary: Families of Steffensen type methods for solving non-linear equations are obtained. One family consists of second order method involving no derivatives, while other consists of third order methods involving only the first derivatives. Also a derivative free third order method is provided. The theory is supported by an example comparing the existing methods with the present one.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Conte, S. D.; De Boor, Carl: Elementary numerical analysis, an algorithmic approach. (1981)
[2] Gander, W.: On halley’s iteration method. Am. math. Mon. 92, No. 2, 131-134 (1985) · Zbl 0574.65041
[3] Kasturiarachi, A. B.: Leap frogging Newton’s method. Int. J. Math. educ. Sci. technol. 33, No. 4, 521-527 (2002)
[4] Ralston, A.: A first course in numerical analysis. (1965) · Zbl 0139.31603