The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A simple method of taking nth roots of integers
ACM SIGSAM Bulletin
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Recently John Fitch [FITC 74] gave an algorithm for computing [A1/n] where A and n are positive integers. His algorithm, based on the classical Newton method, has the virtue of not only being an extremely simple algorithm but it is also fast - both in practice and in theory. One can hardly hope to improve upon an algorithm with such virtues. In this note I will present and analyze the computing time of a variation of the algorithm presented by Fitch. The variation is superior to Fitch's version in the sense that in some cases the theoretical computing time of the new version is dominated by the theoretical computing time of Fitch's version. I do not know which algorithm is faster in practice. I doubt that there is any significant difference for most problems of interest. Certainly Fitch's version is easier to program.