Results 11 to 20 of about 5,022,265 (207)
On numerical stability of continued fractions
Математичні СтудіїThe paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements.
V. Hladun +3 more
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Multidimensional continued fractions and symbolic codings of toral translations [PDF]
Journal of the European Mathematical Society (Print), 2020 It has been a long standing problem to find good symbolic codings for translations on the $d$-dimensional torus that enjoy the beautiful properties of Sturmian sequences like low complexity and good local discrepancy properties (i.e., bounded remainder ...
Val'erie Berth'e +2 more
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Analytic Continued Fractions for Regression: A Memetic Algorithm Approach [PDF]
Expert systems with applications, 2019 We present an approach for regression problems that employs analytic continued fractions as a novel representation. Comparative computational results using a memetic algorithm are reported in this work.
P. Moscato +2 more
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An unusual continued fraction [PDF]
Proceedings of the American Mathematical Society, 2015 We consider the real number $σ$ with continued fraction expansion $[a_0, a_1, a_2,\ldots] = [1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,\ldots]$, where $a_i$ is the largest power of $2$ dividing $i+1$. We compute the irrationality measure of $σ^2$ and demonstrate that $σ^2$ (and $σ$) are both transcendental numbers. We also show that certain partial quotients of
Badziahin, D., Shallit, J.
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Hausdorff dimension of an exceptional set in the theory of continued fractions
Nonlinearity, 2020 In this article we calculate the Hausdorff dimension of the setF(Φ)=x∈[0,1):an+1(x)an(x)⩾Φ(n)for infinitely many n∈Nandan+1(x)
Ayreena Bakhtawar +2 more
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Algorithms, 2023 In the field of Artificial Intelligence (AI) and Machine Learning (ML), a common objective is the approximation of unknown target functions y=f(x) using limited instances S=(x(i),y(i)), where x(i)∈D and D represents the domain of interest.
Pablo Moscato +4 more
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Limit laws for rational continued fractions and value distribution of quantum modular forms [PDF]
Proceedings of the London Mathematical Society, 2019 We study the limiting distributions of Birkhoff sums of a large class of cost functions (observables) evaluated along orbits, under the Gauss map, of rational numbers in (0, 1] ordered by denominators.
S. Bettin, S. Drappeau
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Mathematics, 2021 We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964.
Dan Lascu, Gabriela Ileana Sebe
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Farey Boat: Continued Fractions and Triangulations, Modular Group and Polygon Dissections [PDF]
Jahresbericht Der Deutschen Mathematiker-vereinigung, 2018 We reformulate several known results about continued fractions in combinatorial terms. Among them the theorem of Conway and Coxeter and that of Series, both relating continued fractions and triangulations.
S. Morier-Genoud, V. Ovsienko
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Continued Fractions and Hankel Determinants from Hyperelliptic Curves [PDF]
Communications on Pure and Applied Mathematics, 2019 Following van der Poorten, we consider a family of nonlinear maps that are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus g.
A. Hone
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