A square root algorithm faster than Newton's method for multiprecision numbers, using floating-point arithmetic
Year: 2024
Type: preprint
Abstract: In this paper, an optimized version of classical Bombelli's algorithm for computing integer square roots is presented. In particular, floating-point arithmetic is used to compute the initial guess of each digit of the root, following similar ideas to those used in "The Art of Computer Programming" Vol. 2, p. 4.3.1 for division. A program with an implementation of the algorithm in Java is also presented, and its running time is compared with that of the algorithm provided by the Java standard library, which uses the Newton's method. From tests, the algorithm presented here turns out to be much faster.
Source: arXiv (Cornell University)
Author: Romano, Fabio
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4399694475