共查询到20条相似文献,搜索用时 109 毫秒
1.
回系数的广义根方估计及其模拟 总被引:2,自引:0,他引:2
文献[1,2]中提出了回归系数的根方估计β^(k),当回归自变量间存在复共线关系时,β^(k)较回归系数的最小二乘估计β有所改善。本文将根方估计作一拓广,得出了回归系数的广义根方估计β^(K),其中K为对角阵。文中证明了广义根方估计β^(K)较β^(k)能更有效地改善最小二乘估计,并给出了广义根方估计的显式解,在此基础上,提出了广义根方估计的显式解和一种确定ki的方法。 相似文献
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方差分量谱分解估计的几个性质 总被引:2,自引:0,他引:2
对于线性混合模型中方差分量的估计,虽有多种方法,但一般情况下只有方差分析估计和谱分解估计有显式解,本文就线性混合模型中含两个方差分量的情形,对方差分析估计和谱分解估计进行了比较,证明了在一些条件下两个估计的方差相等,由此推出谱分解估计也具有方差分析估计的某些优良性.文末用实例进一步说明了文中的结果. 相似文献
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特征值问题混合有限元法的一个误差估计 总被引:3,自引:0,他引:3
设(λh,σh,uh)是一个混合有限元特征对.Babuska和Osborn建立了(λh,uh)的误差估计.本文导出了σh的抽象误差估计式.并把该估计式应用于二阶椭圆特征值问题Raviart-Thomas混合有限元格式和重调和算子特征值问题Ciarlet-Raviart混合有限元格式,得到了一些新的误差估计. 相似文献
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本文研究了有界解析函数的n阶导数估计.利用有界解析函数泰勒展开式的系数估计,得到了n阶导数估计的一般式,改进了已有的相关结果. 相似文献
7.
有界正则函数的导数估计 总被引:2,自引:0,他引:2
在这篇文章中,主要讨论了n阶导数的估计式,即对有界正则函数φ(z)=c0 c1z … cnz^n …(在│z│1内正则),从已知的三阶、四阶导数估计式,利用归纳法原理及有界正则函数的性质推出n阶导数的一般估计式,并推出在│z│<1内正则的正实部函数的n阶导数的一般估计式。 相似文献
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本文首先提出了选取回归参数M-估计中函数ρ的一种新原则,然后利用ρ的最佳逼近函数定义了一种新估计-BAME.并证明了其强相合性;讨论了其稳健性,较比通常的M-估计,BAME有以下优点:(1)ρ的选取充分利用了误差的分布信息;(2)具有显式表达,其算法方便;(3)相合性的证明相当于LS-估计的复杂程度,比M-估计简单得多. 相似文献
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王建红 《应用数学与计算数学学报》1993,7(2):90-92
我们在实际中常常遇到满秩长方矩阵的求逆问题,并希望知道所求逆矩阵的精度。目前常用的估计式仅给出了一个粗糙的上界(见[1]),这个上界往往放大许多,因而极不准确,本文给出了实用和较准确的估计式。 相似文献
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Andrew T. Tomerlin 《Integral Equations and Operator Theory》2000,37(3):350-356
An example is given which clarifies the present situation of the operator norm convergence of Trotter-Kato product formula. It shows that the rate of convergence of the formula with respect to the operator norm obtained in [NZ2] is best possible. It also yields a counter-example of the operator norm convergence of the formula in another case. 相似文献
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Olayiwola Otolorin 《International Journal of Mathematical Education in Science & Technology》2013,44(5):539-546
A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is now no need to first ensure a good initial approximation to the root, complex roots are found without necessarily starting from a complex formulation of the iteration formula, and the convergence is faster. The rate of convergence is discussed, and examples given. 相似文献
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We will establish here a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well-known inverse iteration. The formula for the convergence factor is explicit and involves quantities associated with the eigenvalue to which the iteration
converges, in particular the eigenvalue and eigenvector. Residual inverse iteration allows for some freedom in the choice
of a vector w
k
and we can use the formula for the convergence factor to analyze how it depends on the choice of w
k
. We also use the formula to illustrate the convergence when the shift is close to the eigenvalue. Finally, we explain the
slow convergence for double eigenvalues by showing that under generic conditions, the convergence factor is one, unless the
eigenvalue is semisimple. If the eigenvalue is semisimple, it turns out that we can expect convergence similar to the simple
case. 相似文献
14.
基于等距节点积分公式的牛顿迭代法及其收敛阶 总被引:1,自引:0,他引:1
利用等距节点的数值积分公式构造牛顿迭代法的变形格式.我们证明了利用4等分5个节点的Newton-Cotes公式构造的变形牛顿迭代法收敛阶为3,并进一步证明了对于最常用的3等分4节点、5等分6节点、6等分7节点、7等分8节点积分公式,所得到的变形牛顿迭代法收敛阶都是3.最后,本文猜想,利用任意等分的积分公式构造变形牛顿迭代法,所得的迭代格式收敛阶都是3. 相似文献
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第二作者等用一个哲学公式及0.9规格化了收敛过程,从而形象化地解释了概率论与随机计算中的若干定理,使模拟的数值规律化.基于数学软件MATLB进行了大数定律的随机模拟,直观形象地展示了1/n∑_(i=1)~nX_i到数学期望μ的收敛过程,与第二作者等的哲学公式相吻合,从而有助于学生理解和掌握大数定律. 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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This paper introduces an error propagation formula of a certain class of multi-level iterative aggregation-disaggregation (IAD) methods for numerical solutions of stationary probability vectors of discrete finite Markov chains. The formula can be used to investigate convergence by computing the spectral radius of the error propagation matrix for specific Markov chains. Numerical experiments indicate that the same type of the formula could be used for a wider class of the multi-level IAD methods. Using the formula we show that for given data there is no relation between convergence of two-level and of multi-level IAD methods. 相似文献
18.
一种Gauss型求积公式的收敛性 总被引:1,自引:0,他引:1
周志强 《纯粹数学与应用数学》2008,24(3)
构造一种有理插值型求积公式(RIQFs),并证明其收敛性.该方法是Gauss求积公式在有理函数空间(Γ)2n中的推广. 相似文献
19.
Pavel Exner Takashi Ichinose Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2007,57(1):67-81
We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator.
Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive
assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the
situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies. 相似文献
20.
Jean-Paul Berrut 《Numerische Mathematik》2009,112(3):341-361
In former articles we have given a formula for the error committed when interpolating a several times differentiable function
by the sinc interpolant on a fixed finite interval. In the present work we demonstrate the relevance of the formula through
several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence,
improvement of the barycentric formula, rational sinc interpolants (with and without replacement of the (usually unknown)
derivatives with finite differences), convergence acceleration through extrapolation and improvement of one-sided interpolants.
Work partly supported by the Swiss National Science Foundation under grant Nr 200021-116122. 相似文献