On rational functions related to algorithms for a computation of roots. II

• Autorzy: Baran Mirosław

Identyfikatory

DOI

10.5604/01.3001.0013.7275

• Języki publikacji: EN

Abstrakty

EN

We discuss a nice composition properties related to algorithms for computation of N-roots. Our approach gives direct proof that a version of Newton's iterative algorithm is of order 2. A basic tool used in this note are properties of rational function Φ(w; z) = z-w/(z+w), which was used earlier in [1] in the case of algorithms for computations of square roots.

Słowa kluczowe

EN

iterative method; Newton method; rational function

PL

metoda iteracyjna; metoda Newtona; funkcja wymierna

• Wydawca: Państwowa Wyższa Szkoła Zawodowa w Tarnowie
• Czasopismo: Science, Technology and Innovation
• Rocznik: 2019
• Tom: Vol. 7, no. 4
• Strony: 26--29
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Baran Mirosław

• Faculty of Mathematics, Physics and Technical Science, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Bibliografia

• [1] M. Baran, On rational functions related to algorithms for a computation of roots. I, (2019), submited to STI.
• [2] D. Braess, Nonlinear approximation theory, Springer Ser. Comput. Math. Springer, New York (1986).
• [3] E.S. Gawlik, Zolotariev iterations for the matrix square root, SIAM J. Matrix Anal. Appl. 40 (2) (2019), 696–719.
• [4] H. Rutishauser, Betrachtungen zur Quadratwurzeliteration, Monath. f. Math. 67 (1963) 452–464.
• [5] J.F. Traub, Iterative Methods for the Solution of Equations , Prentice- Hall, Englewood Cliffs, NJ (1983).
• [6] A.K. Yeyios, On two sequences of algorithms for approximating square roots, J. of Comp. Appl. Math. 40 (1992), 63–72.