Results 31 to 40 of about 130,314 (163)

On numerical stability of continued fractions

Математичні Студії
The paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements.
V. Hladun, V. Кravtsiv, M. Dmytryshyn, R. Rusyn   +3 more
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Continued Fractions of Square Roots of Natural Numbers

Acta Polytechnica, 2013
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers.
L'ubomíra Balková, Aranka Hrušková
doaj  

Continued Fractions and Hyperbolic Geometry [PDF]

, 2016
This thesis uses hyperbolic geometry to study various classes of both real and complex continued fractions. This intuitive approach gives insight into the theory of continued fractions that is not so easy to obtain from traditional algebraic methods ...
Walker, Mairi
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Positive definite branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2013
Research of the class of branched continued fractions of special form, whose denominators do not equal to zero, is proposed and the connection of such fraction with a certain quadratic form is established.
R.I. Dmytryshyn
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Fractional dimension of some exceptional sets in continued fractions

Comptes Rendus. Mathématique
In this paper, we calculate the Hausdorff dimension of some exceptional sets that emerge from specific constraints imposed on the partial quotients of continued fractions.
Hussain, Mumtaz, Smith, Rebecca, Zhang, Zhenliang   +2 more
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Fast Power System Dynamic Simulation Using Continued Fractions

IEEE Access, 2018
This paper proposes a novel method for power system dynamic simulation that solves power system differential algebraic equations by a semi-analytical and semi-numerical approach using continued fractions.
Chengxi Liu, Bin Wang, Kai Sun
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Asymmetric circular graph with Hosoya index and negative continued fractions

Karpatsʹkì Matematičnì Publìkacìï, 2021
It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem.
T. Komatsu
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Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers [PDF]

, 2015
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear ...
Hone, Andrew N.W.
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Representation of a one class function of two variables by bicontinued fractions

Researches in Mathematics, 2020
Let function $u (z, w) = f (z) h (w)$ be defined on the compact set $\mathbf{K} \subset \mathbb{C}^2$. We study the problem of representation of functions of this class by the product of two continued fractions, which is called a bicontinued fraction ...
M.M. Pahirya
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Outer compositions of hyperbolic/loxodromic linear fractional transfomations

International Journal of Mathematics and Mathematical Sciences, 1992
It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn→f, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0.
John Gill
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