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