Results 211 to 220 of about 74,852 (243)

Generalization of continued fractions. I

Journal of Mathematical Sciences, 2012
We constructed a new algebraic object, namely, recursion fractions of the n th order that are n -dimensional generalizations of continued fractions. For the representation and the study of such fractions, we used paradeterminants and triangular matrices.
D. I. Bodnar, R. A. Zators’kyi
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Generalized continued fractions

Applied Mathematics and Computation, 2000
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Generalized continued fractions

Discrete Mathematics and Applications, 1998
The author considers a generalized continued fraction whose expression has the form \[ a_0+\frac{(-1)^{u_1}}{a_1+{\displaystyle \frac{(-1)^{u_2}}{a_2+{\displaystyle \frac{(-1)^{u_3}}{a_3+\dots}}}}}, \] where \(a_i\in\mathbb R\) (\(i=0,1,2,\dots\)) and \(u_i\in\{0,1\}\) (\(i=1,2,\dots\)). In this paper the concept how to represent a real number \(\alpha\
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Convergence acceleration for generalized continued fractions

Transactions of the American Mathematical Society, 1988
The main result in this paper is the proof of convergence acceleration for a suitable modification (as defined by de Bruin and Jacobsen) in the case of an n n -fraction for which the underlying recurrence relation is of Perron-Kreuser type.
Levrie, Paul, Jacobsen, Lisa
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Stable Evaluation of Generalized Continued Fractions

SIAM Journal on Numerical Analysis, 1981
An error analysis is given for the backward recurrence algorithm for generalized continued fractions. Bounds for the accumulated relative rounding error can be obtained by applying an extension of a technique by Jones and Thron [Math. Comp., 28 (1974), pp. 795–810].
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Generalized continued fractions and ergodic theory

Journal of Mathematical Sciences, 1999
A standard theory of one-dimensional continued fractions is based on the sequential application of the so-called Gauss map and the comparison of the result to zero. The author proposes a generalization of this procedure to the case when one uses some other map, say \(A\), and an arbitrary stopping rule (e.g., the comparison to a given value \(\omega ...
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The Khintchine constants for generalized continued fractions

Applied Mathematics and Computation, 2003
The authors study the limiting behaviour of the Khintchine constants for generalized continued fractions by computer simulations.
Choe, Geon Ho, Kim, Chihurn
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Continuous-time generalized fractional programming

Optimization, 1996
Both parametric and parameter-free necessary and sufficient optimality conditions and several duality models are presented for a class of continuous-time generalized fractional programming problems. These results improve and extend a number of existing results in the area of continuous-time programming and, furthermore, provide continuous-time ...
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Other Generalizations of Continued Fractions

2013
In this chapter we present some other generalizations of regular continued fractions to the multidimensional case. The main goal for us here is to give different geometric constructions related to such continued fractions (whenever possible). We say a few words about Minkowski–Voronoi continued fractions, triangle sequences related to Farey addition, O’
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Markov chains and generalized continued fractions

Journal of Applied Probability, 1992
This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.
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