On Halley’s iteration method. (English) Zbl 0574.65041

Gander, Walter

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

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

Halley’s iteration method; Newton correction; Halley correction; Euler correction