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2018
Basic theory of continued fractions: finite continued fractions (for rational numbers) and infinite continued fractions (for irrational numbers). This also includes computation of the quadratic number with a given periodic continued fraction, conjugate quadratic numbers, and approximation of reals and convergents of continued fractions.
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Basic theory of continued fractions: finite continued fractions (for rational numbers) and infinite continued fractions (for irrational numbers). This also includes computation of the quadratic number with a given periodic continued fraction, conjugate quadratic numbers, and approximation of reals and convergents of continued fractions.
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On Tasoev's continued fractions
Mathematical Proceedings of the Cambridge Philosophical Society, 2003There are a few real irrational numbers which have a regular pattern in their continued fraction expansion. The most prominent examples are real quadratic irrationalities. On the other hand, if one invents continued fractions with some regular pattern, one usually cannot tell much about the numbers which are represented. \textit{B. G.
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Generalized continued fractions
Applied Mathematics and Computation, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algorithms on Continued Fractions
1999Some algorithms for performing arithmetical operations, on line, and fit for parallel and concurrent computation are described and investigated. The algorithms are based on the continued fractions representation of numbers and the continued fraction representation is generalized so as to allow rational quotients (instead of integer quotients).
Octavian Soldea, Azaria Paz
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Noncommutative Continued Fractions
SIAM Journal on Mathematical Analysis, 1971A number of theorems are proved concerning the convergence of continued fractions whose entries are linear operators on a Banach space. These theorems are analogues of some of the well-known results for ordinary continued fractions.
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Convergence of Continued Fractions
Canadian Journal of Mathematics, 1968Let {sn(z)} be a given sequence of linear fractional transformations (or simply l.f.t.'s) of the form1.1and let1.2The sequence of l.f.t.'s {Sn(z)} is called a continued fraction generating sequence (or simply a c.f.g. sequence).
Jones, W. B., Thron, W. J.
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Continued Logarithms and Associated Continued Fractions
Experimental Mathematics, 2016ABSTRACTWe investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical
Jonathan M. Borwein +3 more
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On Recurring Continued Fractions
The Mathematical Gazette, 1934Notation . By ( x/y, X/Y ) = a 1 . a 2 a 3 … are let it be understood that after a vulgar fraction
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Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, 2002
The leading seven terms of a continued fraction were investigated and used to perform on-line arithmetic. A new way to give interval for continued fractions was analyzed. Three important properties were identified for a continued fraction representation of real numbers.
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The leading seven terms of a continued fraction were investigated and used to perform on-line arithmetic. A new way to give interval for continued fractions was analyzed. Three important properties were identified for a continued fraction representation of real numbers.
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The computational complexity of continued fractions
Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81, 1981The paper deals with the complexity of expanding a quolynomial into a continued fraction and shows that the Knuth-Schönage algorithm is essentially optimal with respect to the number of multiplications/divisions used, uniformly in the inputs. The problem consists in computing, given a pair \((A_ 1,A_ 2)\) of polynomials in the indeterminate x over a ...
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