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Zbl 1137.65030
Kanwar, V.; Singh, Sukhjit; Bakshi, S.
Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations. (English)
[J] Numer. Algorithms 47, No. 1, 95-107 (2008). ISSN 1017-1398; ISSN 1572-9265/e

The authors derive the solution for a one parameter family of geometric construction methods using assumptions and theorems to solve nonlinear equations. The developed method is provided with solid mathematical fundamentals and numerical experiments are performed for illustration. Some of the remarks made in the paper are quite encouraging for the researchers in the area.
[Aniket Mahanti (Saint John)]

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: iterative method; Halley's method; Newton's method; nonlinear equations; one-parameter family; Chebyshev's method; super-Halley method; geometric construction methods; numerical exmperiments

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Zentralblatt MATH Berlin [Germany]