共查询到18条相似文献,搜索用时 562 毫秒
1.
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
2.
给出了基于n次Chebyshev多项式零点的Gauss型Hermite求积公式中Cotes数的明显表达式及其当n→∞时的渐近性质.此即给出了P.Turan问题26的解. 相似文献
3.
利用带有积分余项的Taylor公式重新推导了Simpson校正公式,同时给出了其误差的精确表示,而这一结果将优于Simpson校正公式[J]中的误差估计. 相似文献
4.
提出了一类计算定积分的高精度柯特斯校正公式,通过两种方法进行了推导,给出了它的复化公式及其加速公式,并得到了它们的误差估计和收敛阶.数值实验验证了复化柯特斯校正公式及其加速公式的高效性. 相似文献
5.
谢聪聪 《高校应用数学学报(A辑)》2006,21(2):214-222
给出了r阶Sobo lev类KWr[a,b]带权函数的基于给定信息的最佳求积公式和它的误差估计式.这里的给定信息是指:已知函数在给定区间若干点上的函数值和直到r-1阶导数值.对r≤2,得到了最佳求积公式和误差估计式的显式结果.另外还给出了类KW2[a,b]中在节点的导数值为零的函数所组成的子类的相应的最佳求积公式. 相似文献
6.
给出了二项分布、Poisson分布和几何分布高阶矩的递推公式,避免了其它计算方法上的不便与误差. 相似文献
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8.
陶庆生 《高校应用数学学报(A辑)》1992,7(2):177-183
本文提出了广义Bernoulli多项式与广义Bernoulli数,并借此得到了一类含两端点连续阶导数值求积公式的误差渐近式和推广的Euler-Maclaurin求和公式.借助于计算机代数系统进行了公式的机械推导,并列出了部分推导结果. 相似文献
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10.
在本文中,我们首先给出一些基本的结果和一些概念,然后给出单位圆上带Cheby shev权的一些Cauchy主值积分的求积公式,最后给出了它们的误差估计. 相似文献
11.
改进的Cotes公式及其误差分析 总被引:1,自引:1,他引:0
The truncation error of improved Cotes formula is presented in this paper.It also displays an analysis on convergence order of improved Cotes formula.Examples of numerical calculation is given in the end. 相似文献
12.
We present higher-order quadrature rules with end corrections for general Newton–Cotes quadrature rules. The construction is based on the Euler–Maclaurin formula for the trapezoidal rule. We present examples with 6 well-known Newton–Cotes quadrature rules. We analyze modified end corrected quadrature rules, which consist on a simple modification of the Newton–Cotes quadratures with end corrections. Numerical tests and stability estimates show the superiority of the corrected rules based on the trapezoidal and the midpoint rules. 相似文献
13.
P. Bocher H. De Meyer G. Vanden Berghe 《Journal of Computational and Applied Mathematics》1994,50(1-3):145-158
Gregory-type formulae associated with the class of composite Newton—Cotes quadrature rules of the closed type are established. Furthermore, it is shown how these formulae can be extended by introducing mixed interpolation functions which contain a polynomial and a trigonometric part. The case of the modified Gregory rules associated with the composite Simpson quadrature rule is worked out in detail. Also the error term is analysed and the obtained rules are numerically tested. 相似文献
14.
The numerical integration of functions with a boundary-layer component whose derivatives are not uniformly bounded is investigated. The Newton–Cotes formulas as applied to such functions can lead to significant errors. An analogue of Newton–Cotes formulas that is exact for the boundary-layer component is constructed. For the resulting formula, an error estimate that is uniform with respect to the boundary-layer component and its derivatives is obtained. Numerical results that agree with the error estimates are presented. 相似文献
15.
Ayse Alaylioglu 《Journal of Computational and Applied Mathematics》1983,9(4):305-313
A computationally efficient algorithm for evaluating Fourier integrals ∫1?1?(x)eiωxdx using interpolatory quadrature formulas on any set of collocation points is presented. Examples are given to illustrate the performances of interpolatory formulas which are based on the applications of the Fejér, Clenshaw—Curtis, Basu and the Newton—Cotes points. Initially, the formulas for nonoscillatory integrals are generated and then generalizations to finite Fourier integrals are made. Extensions of this algorithm to some other weighted integrals are also considered. 相似文献
16.
Ying-guang Shi 《计算数学(英文版)》1999,17(2):171-178
1.IntroductionThispaperdealswiththegeneralizedGaussianquadratureformulasforChebyshevnodes(of.[2]).Throughoutthepaperweassumethatmandnarepositiveintegers.Asusually,Tn(x)andUn(x)denotethen--thChebyshevpolynomialsofthefirstkindandthesecondkind,respectively.AmonggeneralizedGaussianquadratureformulasoneofthemostimportantcasesistheweightwin(x):~(1~x')[(m ')/']~(" ')/',(1.1)where[rldenotesthelargestinteger5r.In[5]wepointedoutthatifwetakeasnodesofaquadratureformulathezerosof(1--x')Un--100(herewere… 相似文献
17.
M.M. Panja 《Applied mathematics and computation》2011,218(8):4147-4151
This note is concerned with an efficient computation of integrals of products of a smooth function and Daubechies scale function with partial support by using a one-point quadrature rule. The error estimate is obtained. The rule is illustrated by considering an example from the literature. 相似文献
18.
Bernard Bialecki 《Numerische Mathematik》1990,57(1):263-269
Summary A Sinc quadrature rule is presented for the evaluation of Hadamard finite-part integrals of analytic functions. Integration over a general are in the complex plane is considered. Special treatment is given to integrals over the interval (–1,1). Theoretical error estimates are derived and numerical examples are included. 相似文献