共查询到20条相似文献,搜索用时 508 毫秒
1.
G. G. Malachkovs'kii 《Journal of Mathematical Sciences》1998,90(5):2374-2375
We study twin regions of convergence for branched continued fractions and establish an estimate of the rate of convergence;
we construct a counterexample showing that the natural formulation of Thron's convergence criterion for continued fractions
does not extend to branched continued fractions.
Translated fromMatematichni Metodi ta Fiziko-Makhanichni Polya, Vol. 39, No. 2, 1996, pp. 62–64. 相似文献
2.
O. E. Baran 《Journal of Mathematical Sciences》1998,90(5):2348-2351
We study branched continued fractions of a special form with inequivalent variables. We establish a multidimensional analog
of the Vorpits'kii convergence criterion for continued fractions.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 35–38. 相似文献
3.
D. I. Bodnar Kh. Bodeland K. I. Kuchmins'ka O. M. Sus' 《Journal of Mathematical Sciences》1996,79(6):1373-1377
We study two aspects of the stability problem for various types of branching fractions using the domains of the elements,
the region of convergence, and limit-periodic fractions.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 3–7. 相似文献
4.
D. I. Bodnar 《Journal of Mathematical Sciences》1999,97(1):3862-3871
We give a survey of research on the theory of convergence of branched continued fractions.
Translated fromMatematychni Metody ta Fizyko-Mechanichni Polya, Vol. 41, No. 1, 1998, pp. 117–126. 相似文献
5.
A. V. Tsygvintsev 《The Ramanujan Journal》2008,15(3):407-413
We consider the limit periodic continued fractions of Stieltjes type
appearing as Schur–Wall g-fraction representations of certain analytic self maps of the unit disc |w|<1, w∈ℂ. We make precise the convergence behavior and prove the general convergence [2, p. 564] of these continued fractions at
Runckel’s points [6] of the singular line (1,+∞). It is shown that in some cases the convergence holds in the classical sense.
As a result we provide an interesting example of convergence relevant to one result found in the Ramanujan’s notebook [1,
pp. 38–39].
Dedicated to Sacha B. 相似文献
6.
Kh. I. Kuchmins'ka 《Journal of Mathematical Sciences》1998,90(5):2368-2373
For two-dimensional continued fractions we prove the existence and uniqueness of an optimal sequence of value sets corresponding
to an arbitrarily given sequence of element sets. We compute the element set for a given sequence of disk value sets and as
a corollary, give the element sets and value sets that are used in convergence criteria for two-dimensional continued fractions.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 55–61. 相似文献
7.
D. I. Bodnar 《Journal of Mathematical Sciences》1998,90(2):1907-1912
For branched continued fractions with nonnegative components and a fixed or variable number of branchings we establish necessary
and sufficient conditions for their approximants to be well-defined. We study necessary and sufficient conditions for convergence
that are multivariable analogs of the known Seidel-Stern and Stern criteria for continued fractions with positive elements.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 7–13. 相似文献
8.
N. P. Molnar 《Journal of Mathematical Sciences》1998,90(5):2381-2384
Applying recursion relations for the Lauricella hypergeometric functions F
D
Nl
, we construct an expansion of a ratio of these functions in branched continued fractions. We study the convergence of the
resulting expansion in the case of real parameters.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 70–74. 相似文献
9.
In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied
by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce
a property of the measure μ called the (APO2) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types
of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure
μ has the condition (APO2). 相似文献
10.
V. Gupta 《Ukrainian Mathematical Journal》2005,57(12):1892-1900
We estimate the rate of convergence for functions of bounded variation for the Bézier variant of the Szász operators S
n,α
(f,x). We study the rate of convergence of S
n,α
(f,x) in the case 0 < α < 1.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1619–1624, December, 2005. 相似文献
11.
The concept of statistical convergence is one of the most active area of research in the field of summability. Most of the
new summability methods have relation with this popular method. In this paper we generalize the notions of statistical convergence,
(λ, μ)-statistical convergence, (V, λ, μ) summability and (C, 1, 1) summability for a double sequence x = (x
jk
) via ideals. We also establish the relation between our new methods. 相似文献
12.
We characterize convergence in measure of a sequence (fn)n of measurable functions to a measurable function f by elements of c0, which express the quality of convergence of (fn)n to f. This characterization motivates the introduction of a new notion of convergence, called “p-convergence in measure” (p > 0), which is stronger than convergence in measure. We prove the existence of “minimal” elements in c0 which characterize the convergence in measure of (fn)n to f.
相似文献
13.
We consider a family of Newton-type iterative processes solving nonlinear equations in Banach spaces, that generalizes the
usually iterative methods of R-order at least three. The convergence of this family in Banach spaces is usually studied when the second derivative of the
operator involved is Lipschitz continuous and bounded. In this paper, we relax the first condition, assuming that ‖F″(x)−F″(y)‖≤ω(‖x−y‖), where ω is a nondecreasing continuous real function. We prove that the different R-orders of convergence that we can obtain depend on the quasihomogeneity of the function ω. We end the paper by applying the study to some nonlinear integral equations.
This work was supported by the Ministry of Science and Technology (BFM 2002-00222), the University of La Rioja (API-04/13)
and the Government of La Rioja (ACPI 2003/2004). 相似文献
14.
We study the existence and asymptotic convergence when t→+∞ for the trajectories generated by
where is a parametric family of convex functions which approximates a given convex function f we want to minimize, and ε(t) is a parametrization such that ε(t)→ 0 when t→+∞ . This method is obtained from the following variational characterization of Newton's method:
where H is a real Hilbert space. We find conditions on the approximating family and the parametrization to ensure the norm convergence of the solution trajectories u(t) toward a particular minimizer of f . The asymptotic estimates obtained allow us to study the rate of convergence as well. The results are illustrated through
some applications to barrier and penalty methods for linear programming, and to viscosity methods for an abstract noncoercive
variational problem. Comparisons with the steepest descent method are also provided.
Accepted 5 December 1996 相似文献
15.
Fred J. Hickernell Peter Kritzer Frances Y. Kuo Dirk Nuyens 《Numerical Algorithms》2012,59(2):161-183
Quasi-Monte Carlo integration rules, which are equal-weight sample averages of function values, have been popular for approximating
multivariate integrals due to their superior convergence rate of order close to 1/N or better, compared to the order 1/?N1/\sqrt{N} of simple Monte Carlo algorithms. For practical applications, it is desirable to be able to increase the total number of
sampling points N one or several at a time until a desired accuracy is met, while keeping all existing evaluations. We show that although a
convergence rate of order close to 1/N can be achieved for all values of N (e.g., by using a good lattice sequence), it is impossible to get better than order 1/N convergence for all values of N by adding equally-weighted sampling points in this manner. We then prove that a convergence of order N
− α
for α > 1 can be achieved by weighting the sampling points, that is, by using a weighted compound integration rule. We apply our
theory to lattice sequences and present some numerical results. The same theory also applies to digital sequences. 相似文献
16.
Roman A. Polyak 《Computational Optimization and Applications》2006,35(3):347-373
A class Ψ of strictly concave and twice continuously differentiable functions ψ: R → R with particular properties is used for constraint transformation in the framework of a Nonlinear Rescaling (NR) method with
“dynamic” scaling parameter updates. We show that the NR method is equivalent to the Interior Quadratic Prox method for the
dual problem in a rescaled dual space.
The equivalence is used to prove convergence and to estimate the rate of convergence of the NR method and its dual equivalent
under very mild assumptions on the input data for a wide class Ψ of constraint transformations. It is also used to estimate
the rate of convergence under strict complementarity and under the standard second order optimality condition.
We proved that for any ψ ∈ Ψ, which corresponds to a well-defined dual kernel ϕ = −ψ*, the NR method applied to LP generates
a quadratically convergent dual sequence if the dual LP has a unique solution.
This paper is dedicated to Professor Elijah Polak on the occasion of his 75th birthday. 相似文献
17.
H. Aleksanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2012,47(2):86-96
We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions
are found for system’s normalization to guarantee almost everywhere convergence, and convergence in L
p
(T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees
convergence almost everywhere for functions from L
1(T), or uniform convergence for continuous functions. 相似文献
18.
In this paper we give a new convergence analysis of a projective scaling algorithm. We consider a long-step affine scaling
algorithm applied to a homogeneous linear programming problem obtained from the original linear programming problem. This
algorithm takes a fixed fraction λ≤2/3 of the way towards the boundary of the nonnegative orthant at each iteration. The iteration
sequence for the original problem is obtained by pulling back the homogeneous iterates onto the original feasible region with
a conical projection, which generates the same search direction as the original projective scaling algorithm at each iterate.
The recent convergence results for the long-step affine scaling algorithm by the authors are applied to this algorithm to
obtain some convergence results on the projective scaling algorithm. Specifically, we will show (i) polynomiality of the algorithm
with complexities of O(nL) and O(n
2
L) iterations for λ<2/3 and λ=2/3, respectively; (ii) global covnergence of the algorithm when the optimal face is unbounded;
(iii) convergence of the primal iterates to a relative interior point of the optimal face; (iv) convergence of the dual estimates
to the analytic center of the dual optimal face; and (v) convergence of the reduction rate of the objective function value
to 1−λ. 相似文献
19.
Marcel G. de Bruin 《Numerical Algorithms》2007,44(4):367-380
In this paper the classical convergence theorems by Śleszyński-Pringsheim, Worpitzky and Van Vleck for ordinary continued
fractions will be generalized to continued fractions generalizations (along the lines of the Jacobi–Perron algorithm) with
four-term recurrence relations.
相似文献
20.
Di LIU 《Frontiers of Mathematics in China》2012,7(2):305-320
We study jump-diffusion processes with two well-separated time scales. It is proved that the rate of strong convergence to
the averaged effective dynamics is of order O(ɛ
1/2), where ɛ ≪ 1 is the parameter measuring the disparity of the time scales in the system. The convergence rate is shown to be optimal
through examples. The result sheds light on the designing of efficient numerical methods for multiscale stochastic dynamics. 相似文献