- Tytuł:
- On rational functions related to algorithms for a computation of roots. I
- Autorzy:
- Baran, Mirosław
- Powiązania:
- https://bibliotekanauki.pl/articles/93090.pdf
- Data publikacji:
- 2019
- Wydawca:
- Państwowa Wyższa Szkoła Zawodowa w Tarnowie
- Tematy:
-
algorithm
iterative method
polynomial
recurrence relation
algorytm
metoda iteracyjna
wielomian
relacja powtarzalności - Opis:
- 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 Φ(w; z) = z-w/z+w.
- Źródło:
-
Science, Technology and Innovation; 2019, 7, 4; 17-25
2544-9125 - Pojawia się w:
- Science, Technology and Innovation
- Dostawca treści:
- Biblioteka Nauki
Artykuł