共查询到19条相似文献,搜索用时 140 毫秒
1.
2.
Thiele型向量连分式的收敛性定理 总被引:7,自引:3,他引:4
Thiele型向量连分式,不仅可用来解决一元和多元向量有理插值问题[1-3],一元和多元向量切触有理插值问题[3],还可用来研究向量Pade逼近及向量连分式逼近[1,3]。本文给出了这种连分式的收敛性定理,并把著名的Pringsheim定理推广到向量连分式上去。 相似文献
3.
主要证明了几类连分式数列的极限问题.应用实数连续性公理证明了连分数数列的推广形式,几类连分式数列收敛,并得到了它的极限.不仅证明了一些Pell方程的求解问题,而且还把连分式数列收敛问题得到了更广泛深入的推广. 相似文献
4.
5.
首先利用Newton-Pade表中部分序列推导出连分式,提出逆差商算法,算出关于高阶导数与高阶差商的连分式插值余项.接着,构造基于此类连分式的有理求积公式与相应的复化求积公式,算出相应的求积余项,研究表明,在一定条件下,求积公式序列一致收敛于积分真值.然后,为保证连分式计算顺利进行,研究连分式分母非0的充分条件.最后,若干数值算例表明,对某些函数采用新提出的复化有理求积公式计算数值积分,所得结果优于采用Simpson公式. 相似文献
6.
7.
詹棠森 《数学的实践与认识》2012,42(22):156-159
通过倒差商-连分式算法,提出了一种保端点非线性有理参数化拟合算法,通过选取中间点的参数化,利用连分式插值法,得到的拟合函数具有保端点性,规律性和灵活性.实例表明,算法减少了连分式插值迭代次数,避免插值连分式的不存在性,所得到拟合值具有更好的精度,大大提高了计算效率,拟合的误差更具有平稳性,逼近效果更好,并具有较好的预测等方面的应用. 相似文献
8.
10.
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
11.
Martin H. Gutknecht 《Numerische Mathematik》1989,56(6):547-589
Summary We discuss first the block structure of the Newton-Padé table (or, rational interpolation table) corresponding to the double sequence of rational interpolants for the data{(z
k, h(zk)}
k
=0. (The (m, n)-entry of this table is the rational function of type (m,n) solving the linearized rational interpolation problem on the firstm+n+1 data.) We then construct continued fractions that are associated with either a diagonal or two adjacent diagonals of this Newton-Padé table in such a way that the convergents of the continued fractions are equal to the distinct entries on this diagonal or this pair of diagonals, respectively. The resulting continued fractions are generalizations of Thiele fractions and of Magnus'sP-fractions. A discussion of an some new results on related algorithms of Werner and Graves-Morris and Hopkins are also given.Dedicated to the memory of Helmut Werner (1931–1985) 相似文献
12.
Khrystyna Kuchmins"ka 《Acta Appl Math》2000,61(1-3):175-183
By the method of majorant fractions and equivalent transformations, the analogies of leszyski–Pringsheim criteria for two-dimensional continued fractions are obtained. 相似文献
13.
《Journal of Computational and Applied Mathematics》1999,106(2):299-305
Euler's Connection describes an exact equivalence between certain continued fractions and power series. If the partial numerators and denominators of the continued fractions are perturbed slightly, the continued fractions equal power series plus easily computed error terms. These continued fractions may be integrated by the series with another easily computed error term. 相似文献
14.
In this paper, I examine Euler's early work on the elementary properties of continued fractions in the 1730s, and investigate its possible links to previous writings on continued fractions by authors such as William Brouncker. By analysing the content of Euler's first paper on continued fractions, ‘De fractionibus continuis dissertatio’ (1737, published 1744) I conclude that, contrary to what one might expect, Euler's work on continued fractions initially arose not from earlier writings on continued fractions, but from a wish to solve the Riccati differential equation. 相似文献
15.
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
16.
《Expositiones Mathematicae》2021,39(3):480-499
In this paper we recast the Serret theorem about a characterization of palindromic continued fractions in the context of polynomial continued fractions. Then, using the relation between symmetric tridiagonal matrices and polynomial continued fractions we give a quick exposition of the mathematical aspect of the perfect quantum state transfer problem. 相似文献
17.
Oleg Karpenkov 《manuscripta mathematica》2011,134(1-2):157-169
In this paper we introduce a link between geometry of ordinary continued fractions and trajectories of points that moves according to the second Kepler law. We expand geometric interpretation of ordinary continued fractions to the case of continued fractions with arbitrary elements. 相似文献
18.
Pakwan Riyapan Vichian Laohakosol Tuangrat Chaichana 《Periodica Mathematica Hungarica》2006,52(2):51-72
Summary Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered
by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method.
The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded
by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization.
Similar results are also established for continued fractions in the field of formal series over a finite base field. 相似文献
19.
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