共查询到15条相似文献,搜索用时 77 毫秒
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我们讨论了如下形式的向量值连分式这里bn=(bn1,bn2,…,bnd)满足Samelson逆,而且an,bn1,bn2,…,bnd均为正.给出了形如(#)的向量值连分式收敛的充分和必要条件,同时给出了收敛时的截断误差估计. 相似文献
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利用Lu等人通过连分式修正更快收敛的欧拉常数数列及其相关余项式,进一步采用Levin变换进行二次加速,特别是在克服舍入误差的情况下,就能更有效地计算出欧拉常数的高精度数值结果. 相似文献
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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
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利用截断的Thiele连分式,本文给出了一个求解非线性单变量方程的单步迭代方法,并证明了所提出的迭代方法具有四阶收敛性.最后,本文通过一些数值例子说明了所提出的方法的有效性和表现. 相似文献
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顾郁枫 《应用数学与计算数学学报》2002,16(2):57-60
本文借助于基于广义逆矩阵Thiele-型连分式插值的计算公式,建立了多项式矩阵求逆的一个新方法。关于多项式矩阵求逆的一个实例给出以说明本文的结果。 相似文献
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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
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Stefan Paszkowski 《Numerical Algorithms》2003,32(2-4):193-247
The tails of a continued fraction satisfy a bilinear recurrent equation. Transforming iteratively these tails (in a special manner) as well as these equations one may obtain finally, for a given fraction, a new, so-called diagonal continued fraction (DF) having the same value. For many important classes of continued fractions the DF has a calculable analytical form and converges qualitatively faster. Using the same method one may transform some hypergeometrical series directly into fast convergent DFs. 相似文献
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一类连分数的有理逼近 总被引:2,自引:0,他引:2
设f(n)是非负函数,k,b,s_i,t_i(i=1,2,…)是正常数,研究形如[a_0,a_1,a_2…]=[■]_m~∞=0和[■]_n~∞=1的连分数有理逼近的下界. 相似文献
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This is an expository article which contains alternative proofs of many theorems concerning convergence of a continued fraction to a holomorphic function. The continued fractions which are studied are continued fractions of the form
where {a
n
}, {b
n
} are real sequences with a
n
>0 (associated continued fractions). The proofs rely on the properties of the resolvent (–T)–1, where T is the symmetric tridiagonal operator corresponding to {a
n
} and {b
n
}, and avoid most of technical aspects of earlier work. A variety of well-known results is proved in a unified way using operator methods. Many proofs can be regarded as functional analytic proofs of important classical theorems. 相似文献
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M. O. Avdeeva 《Functional Analysis and Its Applications》2004,38(2):79-87
We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics. 相似文献