A generalization of the simple continued fraction algorithm
نویسندگان
چکیده
منابع مشابه
A Multidimensional Continued Fraction Generalization of Stern’s Diatomic Sequence
Continued fractions are linked to Stern’s diatomic sequence 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, . . . (given by the recursion relations α2n = αn and α2n+1 = αn + αn+1, where α0 = 0 and α1 = 1), which has long been known. Using a particular multidimensional continued fraction algorithm (the Farey algorithm), we generalize the diatomic sequence to a sequence of numbers that quite naturally can be terme...
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One of the most interesting proofs is due to Hermite; it arose as a byproduct of his proof of the transcendence of e in [5]. (See [6] for an exposition by Olds.) The purpose of this note is to present an especially short and direct variant of Hermite’s proof and to explain some of the motivation behind it. Consider any continued fraction [a0, a1, a2, . . .]. Its ith convergent is defined to be ...
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It has been believed that the continued fraction expansion of (α, β) (1, α, β is a Q-basis of a real cubic field) obtained by the modified JacobiPerron algorithm is periodic. We conducted a numerical experiment (cf. Table B, Figure 1 and Figure 2) from which we conjecture the non-periodicity of the expansion of (⟨ 3 √3⟩, ⟨ 3 √9⟩) (⟨x⟩ denoting the fractional part of x). We present a new algorit...
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در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...
On Jacobi's Extension of the Continued Fraction Algorithm.
1 Adams, W. S., and Kohlschiitter, A., Mt. Wilson Contr. No. 62, Astroph. J., Chicago, Ill., 36, 1912, (293-321). 2 Campbell, W. W., and Wright, W. H., Lick Obs. Bul. No. 8, Berkeley, Cal., 1901. ' Scheiner, J., Astronomical Spectroscopy (Frost), Boston, Mass., 1894, p. 290. 4Michelson, W., Astroph. J., Chicago, Ill., 13, 1901, (192-198). s Paddock, G. F., Pub. Astr. Soc. Pac., San Francisco, C...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0480367-5