共查询到19条相似文献,搜索用时 93 毫秒
1.
基于Thiele型连分式构造求积公式,这类求积公式能再生由Thiele型连分式前三项渐近式的线性组合所表示的任意有理函数,接着算出求积余项,并推导出分母在给定区间上无零点的充分条件.更进一步,通过等分给定区间,构造相应的复化求积公式,并算出求积余项.研究表明,在若干条件满足的前提下,复化求积公式序列能一致收敛于积分真值,一些数值算例说明了这一点. 相似文献
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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
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本文首先基于新的非张量积型偏逆差商递推算法,分别构造奇数与偶数个插值节点上的二元连分式散乱数据插值格式,进而得到被插函数与二元连分式间的恒等式.接着,利用连分式三项递推关系式,提出特征定理来研究插值连分式的分子分母次数.然后,数值算例表明新的递推格式可行有效,同时,通过比较二元Thiele型插值连分式的分子分母次数,发现新的二元插值连分式的分子分母次数较低,这主要归功于节省了冗余的插值节点. 最后,计算此有理函数插值所需要的四则运算次数少于计算径向基函数插值. 相似文献
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本文第一节利用 Samelson逆、混合偏差商以及 Thiele-型分叉连分式构造三元向量值混合有理插值 ,第二节给出了一种计算三元向量值混合有理插值的算法 ,第三节给出了一个数值例子 . 相似文献
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中点公式余项“中间点”的渐进性定理及其应用 总被引:6,自引:0,他引:6
李毅夫 《数学的实践与认识》2005,35(7):236-240
给出中点公式余项“中间点”的渐进性定理及其应用.研究表明,本文定理对于探讨有关求积公式的稳定性及其改进,具有十分重要的作用. 相似文献
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Cotes数值求积公式的校正 总被引:2,自引:0,他引:2
本文研究了Cotes数值求积公式代数精度的问题,给出了Cotes求积公式余项"中间点"的渐进性定理.利用该定理得到了改进的Cotes求积公式,并证明了改进后的Cotes求积公式比原来的公式具有较高的代数精度. 相似文献
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王家正 《应用数学与计算数学学报》2006,20(2):77-82
Stieltjes型分叉连分式在有理插值问题中有着重要的地位,它通过定义反差商和混合反差商构造给定结点上的二元有理函数,我们将Stieltjes型分叉连分式与二元多项式结合起来,构造Stieltje- Newton型有理插值函数,通过定义差商和混合反差商,建立递推算法,构造的Stieltjes-Newton型有理插值函数满足有理插值问题中所给的插值条件,并给出了插值的特征定理及其证明,最后给出的数值例子,验证了所给算法的有效性. 相似文献
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根据积分第一中值定理的中间点 ξ的渐近性质推导出一种单节点数值求积公式 ;证明余项的表达式 ;进行数值实验 .此求积公式还适于瑕积分的数值计算 . 相似文献
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By using the difference formula for approximations of two-dimensional continued fractions, the method of fundamental inequalities, the Stieltjes–Vitali theorem, and generalizations of divided and inverse differences, we estimate the accuracy of approximations of two-dimensional continued fractions with complex elements by their convergents and obtain estimates for the real and imaginary parts of remainders of two-dimensional continued fractions. We also prove an analog of the van Vleck theorem and construct an interpolation formula of the Newton–Thiele type. 相似文献
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The relation between continued fractions and Berlekamp's algorithm was studied by some researchers. The latter is an iterative
procedure proposed for decoding BCH codes. However, there remains an unanswered question wheter each of the iterative steps
in the algorithm can be interpreted in terms of continued fractions. In this paper, we first introduce the so-called refined
convergents to the continued fraction expansion of a binary sequence S, and then give a thorough answer to the question in
the context of Massey's linear feedback shift register synthesis algorithm which is equivalent to that of Berlekamp, and at
last we prove that there exists a one-to-one correspondence between then-th refined convergents and the lengthn segments. 相似文献
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Jorge D. Samur 《Transactions of the American Mathematical Society》1996,348(4):1411-1428
It is shown that if a certain condition on the variances of the partial sums is satisfied then a theorem of Philipp and Stout, which implies the asymptotic fluctuation results known for independent random variables, can be applied to some quantities related to continued fractions. Previous results on the behavior of the approximation by the continued fraction convergents to a random real number are improved.
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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
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Nadir Murru 《The Ramanujan Journal》2017,44(1):115-124
Multidimensional continued fractions generalize classical continued fractions with the aim of providing periodic representations of algebraic irrationalities by means of integer sequences. We provide a characterization for periodicity of Jacobi–Perron algorithm by means of linear recurrence sequences. In particular, we prove that partial quotients of a multidimensional continued fraction are periodic if and only if numerators and denominators of convergents are linear recurrence sequences, generalizing similar results that hold for classical continued fractions. 相似文献
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P. van der Cruyssen 《Journal of Computational and Applied Mathematics》1982,8(3):179-186
Four algorithms for the computation of convergents of generalized continued fractions are defined and studied with respect to numerical effort, error propagation, and practical aspects. Some conclusions from numerical tests are deduced. 相似文献
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This paper is a sequel to our previous work in which we found a combinatorial realization of continued fractions as quotients of the number of perfect matchings of snake graphs. We show how this realization reflects the convergents of the continued fractions as well as the Euclidean division algorithm. We apply our findings to establish results on sums of squares, palindromic continued fractions, Markov numbers and other statements in elementary number theory. 相似文献
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G. Claessens 《Numerische Mathematik》1976,27(1):77-83
Summary A new algorithm is derived for computing continued fractions whose convergents form the elements of the osculatory rational interpolation table. 相似文献
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A. Bultheel 《Journal of Computational and Applied Mathematics》1980,6(4):259-266
It is known [26] that the Viskovatoff algorithm can be generalized to cover the computation of continued fractions whose successive convergents form the Padé approximants of a descending staircase or diagonal, even in the case of a non-normal Padé table. It is the intention of the author to generalize this idea to other paths of the Padé table and in this way link together some algorithms scattered in literature. 相似文献