Continued fraction algorithms, functional operators, and structure constants
نویسندگان
چکیده
منابع مشابه
Continued Fraction Algorithms, Functional Operators, and Structure Constants Continued Fraction Algorithms, Functional Operators, and Structure Constants 1 Continued Fraction Algorithms, Functional Operators, and Structure Constants
Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2-dimensional generalization. This paper surveys the main properties of functional operators, |transfer operators| due to Ruelle and Mayer (also following L evy, Kuzmin, Wirsing, Hensley, and others) that describe...
متن کاملContinued Fraction Algorithms, Functional Operators, and Structure Constants
Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2-dimensional generalization. This paper surveys the main properties of functional operators, |transfer operators| due to Ruelle and Mayer (also following L evy, Kuzmin, Wirs-ing, Hensley, and others) that describ...
متن کاملComputation of a Class of COntinued Fraction Constants
We describe a class of algorithms which compute in polynomial– time important constants related to the Euclidean Dynamical System. Our algorithms are based on a method which has been previously introduced by Daudé Flajolet and Vallée in [10] and further used in [13, 32]. However, the authors did not prove the correctness of the algorithm and did not provide any complexity bound. Here, we descri...
متن کامل$3$-dimensional Continued Fraction Algorithms Cheat Sheets
Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of R. We consider multidimensional continued fraction algorithms that acts symmetrically on the positive cone R+ for d = 3. We include well-known and old ones (Poincaré, Brun, Selmer, Fully Subtrac...
متن کاملSome aspects of multidimensional continued fraction algorithms
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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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1998
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(97)00123-0