Some new variants of Newton’s method. (English) Zbl 1065.65067

Özban, A. Y.

Appl. Math. Lett. 17, No. 6, 677-682 (2004).

The paper is devoted to the study of some hybrid Newton-type methods of the form \[ x_{n+1}=x_n-\frac{f(x_n)}{E(f,x_n)}, \] where \(E(f,x_n)\) is either \(\frac{2f'(x_n)f'(z_{n+1})}{f'(x_n)+f'(z_{n+1})}\) or \(f'((x_n+x_{n+1})/2)\), with \[ z_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}. \]

Reviewer: Vasile Berinde (Baia Mare)

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

Newton’s method; harmonic mean Newton’s method; midpoint Newton’s method; convergence

References:

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