Abstract
Fromf(x)=x n −r and a polynomialQ p (y)=∑ pi=0 a i y i, we consider Newton's method to solveF p (x)=Q p (f(x))=0. We obtain convergent iterative methods of orderp+1 to findr 1/n for arbitraryp.
Zusammenfassung
Fürf(x)=x n −r und ein PolynomQ p (y)=∑ pi=0 a i y i betrachten wir das Newton-Verfahren fürF p (x)=Q p (f(x))=0. Wir erhalten so konvergente iterative Verfahren der Ordnungp+1 fürr 1/n, mit beliebigemp.
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Dubeau, F. Algorithms forn-th root approximation. Computing 57, 365–369 (1996). https://doi.org/10.1007/BF02252255
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DOI: https://doi.org/10.1007/BF02252255