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High order algorithms for calculating roots

Published online by Cambridge University Press:  17 October 2016

Ulrich Abel
Ulrich Abel*
Affiliation:
Technische Hochschule Mittelhessen, Department MND, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany e-mail: Ulrich.Abel@mnd.thm.de
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Extract

In a recent Note [1] Michael D. Hirschhorn presented high order algorithms for calculating numerically square roots and cube roots. In particular, he obtained the method

(1)

with , where the convergence is of tenth order:

We recall his idea in the case of an arbitrary square root with a > 0. Let p ⩾ 2 be a fixed integer. Our starting point is the relation

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The Mathematical Gazette , Volume 100 , Issue 549 , November 2016 , pp. 420 - 428
Copyright
Copyright © Mathematical Association 2016 

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References

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