A new multidimensional continued fraction algorithm
نویسندگان
چکیده
منابع مشابه
A new multidimensional continued fraction algorithm
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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In his paper "Multidimensional continued fractions" {Ann. Univ. Sei. Budapest. EOtvOs Sect. Math., y. 13, 1970, pp. 113-140), G. Szekeres introduced a new higher dimensional analogue of the ordinary continued fraction expansion of a single real number. The Szekeres algorithm associates with each fc-tuple (a»,..., ak) of real numbers (satisfying 0 < a< 1) a sequence bx, b2,... of positive intege...
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The classical continued fraction is generalized for studying the rational approximation problem on multi-formal Laurent series in this paper, the construction is called m-continued fraction. It is proved that the approximants of an m-continued fraction converge to a multiformal Laurent series, and are best rational approximations to it; conversely for any multi-formal Laurent series an algorith...
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Many kinds of algorithms of continued fraction expansions of dimension s(≥ 2) have been studied starting with K.G.J.Jacobi(1804-1851), for example, see [14]. For s = 1, we know Lagrange’s theorem related to periodic continued fractions and real quadratic irrationals. But, even for real cubic irrationalities, there appeared no suitable algorithms (of dimension 2). In this section, we roughly exp...
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We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arnoux and Nogueira. We also apply the same method on the unsorted version of Brun algorithm and Cassaigne algorithm. We illustrate some experimentations on the domain of the natural extension of those algorithms. For so...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2009
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-09-02217-0