On rational functions related to algorithms for a computation of roots
Part 1
DOI:
https://doi.org/10.5604/01.3001.0013.7274Keywords:
algorithms, iterative methods, polynomials, recurrence relationsAbstract
We discuss a less known but surprising fact: a very old algorithm for computing square root known as the Bhaskara-Brouncker algorithm contains another and faster algorithms. A similar approach was obtained earlier by A.K. Yeyios [8] in 1992. By the way, we shall present a few useful facts as an essential completion of [8]. In particular, we present a direct proof that k – th Yeyios iterative algorithm is of order k. We also observe that Chebyshev polynomials Tn and Un are a special case of a more general construction. The most valuable idea followed this paper is contained in applications of a simple rational function 
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