Concerning the rate of convergence of Newton’s process. (English) Zbl 0314.65023

Pták, Vlastimil

Commentat. Math. Univ. Carol. 16, 699-705 (1975).

Summary: The author establishes an explicit formula for the partial sums \(x+\omega(x)+\ldots+\omega^(n)x\) where \(\omega\) is the rate of convergence obtained by the author [Numer. Math. 25, 279–285 (1976; Zbl 0304.65037)] for the Newton’s process \(\omega(x) =\frac{x^2}{2(x^2+d)^{1/2}}\).

MSC:

65H05	Numerical computation of solutions to single equations
65H10	Numerical computation of solutions to systems of equations
65J05	General theory of numerical analysis in abstract spaces

Keywords:

nondiscrete mathematical induction; rate of convergence; Newton process

Citations:

Zbl 0304.65037