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EnglishIn this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate subsequences (x_g_n) for every linear recurrent sequence (g_n) of order 2. Using these formulas we prove that some approximation methods, as secant, Newton, Halley and Householder methods, can generate subsequences of (xn). Moreover, interesting properties on Fibonacci numbers arise as an application. Finally, we apply all the results to the convergents of a particular continued fraction which represents quadratic irrationalities.
| Titolo: | Accelerations of Generalized Fibonacci Sequences | |
| Autori Riconosciuti: | ||
| Autori: | Marco Abrate; Stefano Barbero; Umberto Cerruti; Nadir Murru | |
| Data di pubblicazione: | 2011 | |
| Abstract: | In this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate subsequences (x_g_n) for every linear recurrent sequence (g_n) of order 2. Using these formulas we prove that some approximation methods, as secant, Newton, Halley and Householder methods, can generate subsequences of (xn). Moreover, interesting properties on Fibonacci numbers arise as an application. Finally, we apply all the results to the convergents of a particular continued fraction which represents quadratic irrationalities. | |
| Volume: | 49 | |
| Pagina iniziale: | 255 | |
| Pagina finale: | 266 | |
| URL: | http://arxiv.org/pdf/1301.3477.pdf http://www.fq.math.ca/ | |
| Parole Chiave: | Fibonacci sequences; approximation methods; secant; Newton; Halley; Householder | |
| Rivista: | THE FIBONACCI QUARTERLY | |
| Appare nelle tipologie: | 03A-Articolo su Rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Accelerations of Generalized Fibonacci Sequences.pdf | POSTPRINT (VERSIONE FINALE DELL’AUTORE) | Accesso aperto | Open Access Visualizza/Apri |
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