Gander, Walter On Halley’s iteration method. (English) Zbl 0574.65041 Am. Math. Mon. 92, 131-134 (1985). The author considers the iteration method \(x_{k+1}=F(x_ k)\) where \(F(x)=x-(f(x)/f'(x))\cdot G(x)\) for computing a zero of f. He shows that E. Halley’s method [Methodus Nova, Accurata et Facilis Inveniendi Radices Aequationum Quarumcumque Generaliter, Sine Praevia Reductione, Philos. Trans. Roy. Soc. London, 18, 136-148 (1694)] can be derived by choosing G(x) appropriately. Reviewer: G.Alefeld Cited in 2 ReviewsCited in 67 Documents MSC: 65H05 Numerical computation of solutions to single equations Keywords:Halley’s iteration method; Newton correction; Halley correction; Euler correction PDF BibTeX XML Cite \textit{W. Gander}, Am. Math. Mon. 92, 131--134 (1985; Zbl 0574.65041) Full Text: DOI OpenURL