共查询到20条相似文献,搜索用时 46 毫秒
1.
Paul Levrie 《Numerische Mathematik》1989,56(5):501-512
Summary In this paper we present a method of convergence acceleration for the calculation of non-dominant solutions of second-order linear recurrence relations for which the coefficients satisfy certain asymptotic conditions. It represents an improvement of the method recently proposed by Jacobsen and Waadeland [3, 4] for limit periodic continued fractions. For continued fractions the method corresponds to a repeated application of the Bauer-Muir transformation. Some examples and a generalization to non-homogeneous recurrence relations are given. 相似文献
2.
The aim of this work is to give some criteria on the convergence of vector valued continued fractions defined by Samelson inverse. We give a new approach to prove the convergence theory of continued fractions. First, by means of the modified classical backward recurrence relation, we obtain a formula between the m-th and n-th convergence of vector valued continued fractions. Second, using this formula, we give necessary and sufficient conditions for the convergence of vector valued continued fractions. 相似文献
3.
《Journal of Computational and Applied Mathematics》1997,78(1):3-8
An alternative (equivalent) definition of continued fractions in terms of a group representation is introduced. With this definition, continued fractions are considered as sequences in a topological group, converging (in some sense) to its boundary. This point of view yields an alternative (equivalent) proof for Lane's convergence theorem for periodic continued fractions. 相似文献
4.
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
5.
6.
Zuosheng Hu Angelo B. Mingarelli 《Proceedings of the American Mathematical Society》2004,132(2):417-428
We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.
7.
Roger Alexander. 《Mathematics of Computation》2003,72(244):1947-1961
Aitken extrapolation, applied to certain sequences, yields the even-numbered subsequence of the original. We prove that this is true for sequences generated by iterating a linear fractional transformation, and for some sequences of convergents of the regular continued fractions of certain quadratic irrational numbers. 相似文献
8.
9.
《Journal of Computational and Applied Mathematics》2001,127(1-2):17-65
Complex Jacobi matrices play an important role in the study of asymptotics and zero distribution of formal orthogonal polynomials (FOPs). The latter are essential tools in several fields of numerical analysis, for instance in the context of iterative methods for solving large systems of linear equations, or in the study of Padé approximation and Jacobi continued fractions. In this paper we present some known and some new results on FOPs in terms of spectral properties of the underlying (infinite) Jacobi matrix, with a special emphasis to unbounded recurrence coefficients. Here we recover several classical results for real Jacobi matrices. The inverse problem of characterizing properties of the Jacobi operator in terms of FOPs and other solutions of a given three-term recurrence is also investigated. This enables us to give results on the approximation of the resolvent by inverses of finite sections, with applications to the convergence of Padé approximants. 相似文献
10.
It is well known that solutions of the rational interpolation problem or Newton-Padé approximation problem can be represented with the help of continued fractions if certain normality assumptions are satisfied. By comparing two interpolating continued fractions, one obtains a recursive QD-type scheme for computing the required coefficients. In this paper a uniform approach is given for two different interpolating continued fractions of ascending and descending type, generalizing ideas of Rutishauser, Gragg, Claessens, and others. In the nonnormal case some of the interpolants are equal yielding so-called singular blocks. By appropriate “skips” in the Newton-Padé table modified interpolating continued fractions are derived which involve polynomials known from the Kronecker algorithm and from the Werner-Gutknecht algorithm as well as from the modification of the cross-rule proposed recently by the authors. A corresponding QD-type algorithm for the nonnormal Newton-Padé table is presented. Finally, the particular case of Padé approximation is discussed where—as in Cordellier's modified cross-rule—the given recurrence relations become simpler. 相似文献
11.
In this paper, we study a very simple three term recurrence relation involving the discontinuous Heaviside step function. One reason for studying such an relation is that solutions of our recurrence relation are steady state distributions in some basic neural network models. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by combining combinatorial elimination technique as well as existence arguments for linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 9. Some periodic solutions with periods 15, 18, 42 and 72 can also be found, but exhaustive results are not yet available. 相似文献
12.
In this paper, we study a very simple three term recurrence relation involving the discontinuous Heaviside step function. One reason for studying such an relation is that solutions of our recurrence relation are steady state distributions in some basic neural network models. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by combining combinatorial elimination technique as well as existence arguments for linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 8. Some periodic solutions with periods 12, 20 and 36 can also be found, but exhaustive results are not yet available. 相似文献
13.
In this paper, three-term recurrence relations for branched continued fractions are determined. Based on the algorithm of
partial inverse differences in tensor-product-like manner, the finite branched continued fractions can be applied to rational
interpolation over pyramid-typed grids in R
3. By means of the three-term recurrence relations, a characterization theorem is valid. Then an error estimation is worked
out. Based on the relationship between the partial inverse differences and partial reciprocal ones, and the partial reciprocal
derivatives as well, the BCFs osculatory interpolation with its algorithm is stated which shows it feasibility of partial
derivable functions in BCFs expansion at one point. 相似文献
14.
O. N. Karpenkov 《Functional Analysis and Its Applications》2004,38(2):102-110
The notion of equivalence of multidimensional continued fractions is introduced. We consider some properties and state some conjectures related to the structure of the family of equivalence classes of two-dimensional periodic continued fractions. Our approach to the study of the family of equivalence classes of two-dimensional periodic continued fractions leads to revealing special subfamilies of continued fractions for which the triangulations of the torus (i.e., the combinatorics of their fundamental domains) are subjected to clear rules. Some of these subfamilies are studied in detail; the way to construct other similar subfamilies is indicated. 相似文献
15.
本文建立了Clifford连分式的三项递推关系和Pincherle's定理,并给出了它们的应用,也获得了关于Clifford连分式的矩阵递推关系的最小解的几个性质. 相似文献
16.
《Journal of Approximation Theory》2003,120(1):136-152
We discuss the properties of matrix-valued continued fractions based on Samelson inverse. We begin to establish a recurrence relation for the approximants of matrix-valued continued fractions. Using this recurrence relation, we obtain a formula for the difference between mth and nth approximants of matrix-valued continued fractions. Based on this formula, we give some necessary and sufficient conditions for the convergence of matrix-valued continued fractions, and at the same time, we give the estimate of the rate of convergence. This paper shows that some famous results in the scalar case can be generalized to the matrix case, even some of them are exact generalizations of the scalar results. 相似文献
17.
Antonio-Jesús López-Moreno José-Manuel Latorre-Palacios 《Journal of Mathematical Analysis and Applications》2011,380(2):425-439
In this paper we study localization results for classical sequences of linear positive operators that are particular cases of the generalized Baskakov/Mastroianni operators and also for certain class of composite operators that can be derived from them by means of a suitable transformation. Amongst these composite operators we can find classical sequences like the Meyer-König and Zeller operators and the Bleimann, Butzer and Hahn ones. We extend in different senses the traditional form of the localization results that we find in the classical literature and we show several examples of sequences with different behavior to this respect. 相似文献
18.
Gen-Qiang Wang 《Journal of Difference Equations and Applications》2013,19(2):261-304
Doubly periodic travelling waves can be used to describe dynamic patterns of signals that govern movements of animals. In this paper, we study the existence of such waves in cellular networks involving the discontinuous Heaviside step function. This is done by finding ω-periodic solutions of an accompanying recurrence relation with a priori unknown parameters and the Heaviside function. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by means of symmetry, combinatorial techniques and accompanying linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 6. Our techniques are new and good for other periodic solutions with relatively small periods. 相似文献
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20.
《Journal of Computational and Applied Mathematics》1988,23(1):63-85
The approximants mentioned in the title are related to vector-valued continued fractions and the vector ϵ-algorithm devised by Wynn in 1963. Here we establish a unitary invariance property of these approximants and describe how the classical (1-dimensional) Padé approximants can be obtained as a special case. The main results of the paper consist of De Montessus—De Ballore type convergence theorems for row sequences (having fixed denominator degree) of vector-valued approximants to meromorphic vector functions. 相似文献