通过适当选取正则参数，证明了正则解具有最优的渐近收敛阶。
By apriori choosing regularization parameter, optimal convergence order of the regularized solution is obtained.
经过详细分析，证明了在此种三角网格剖分下h 1范数的收敛阶数仍是最优的。
After some detailed analysis, the optimal order convergence in H1-norm is obtained under this type of triangulation.
推广了迭代算法收敛分析中的Q 收敛阶的概念，据此给出了算法效率的一种一般的度量。
The definition of Q rates of convergence in iterative algorithms is extened and the efficiency measure is developed.
构造了一类适用于并行计算的并行块方法，分析了该类方法的收敛性，得到其最低可达收敛阶。
A class of parallel block methods which are suitable for integrating these equations on parallel computers are proposed.
随机延迟微分方程数值方法中欧拉方法是唯一较为成熟、有效的方法，但欧拉方法的收敛性差，其收敛阶仅为二分之一。
Only the Euler method is popular and efficient among the numerical methods for the stochastic delay differential equations, but its order of convergence is only 1/2.
配置法是以满足纯插值约束条件的方式，寻求算子方程近似解的方法，且具有无需计算数值积分、计算量小、收敛阶高等优点。
The collocation method is a numerical method which search for the approximate solution of the equation by way of meeting pure interpolation condition.
另一方面，采用传统迭代子和共轭梯度法作为光滑子，我们证明了瀑布型多重网格法对一、二维非线性椭圆边值问题，在能量范数下，均可获得最优收敛阶。
Onthe other hand, with traditional iterations and the conjugate gradient(CG) as smoothers, we can show the optimal convergence rate of the cascadic method in energy norm for 1-D and 2-D cases.
牛顿迭代法也称为牛顿切线法，是解非线性方程的一种方法，通过实例对该方法进行了介绍，包括其理论依据、误差估计、收敛阶数、迭代法初始值的选取规则等。
This paper introduces the method with examples to explain it, including its connective knowledge, theory bases, error estimation, convergence order, and the choosing rule for starting value of it.
该算法具有二阶收敛性，其有效性为文中展示的图像分离测试效果所证实。
The algorithm is two-order convergent, Whose validity is confirmed by effect of the image separation test.
通过形式化描述和分析CSCM机制的系统模型和运行模型，证明了CSCM具有一阶线性的消息复杂度和收敛时间。
By formalizing description of system model and running model of CSCM mechanism, the usability and extensibility of the system is given, and the message complexity and convergence time is proved.
迭代公式II也是一种单步迭代公式，在单根附近具有三阶收敛速度；
The second iterative formula(II) is also one-step iterative formula and has three order convergence at single root.
给出二阶模糊随机变量和模糊随机变量序列均方收敛的概念，证明了一些相关的性质。
The concepts of second order fuzzy random variables and mean square convergence of sequences of fuzzy random variables are introduced. Some related properties are proved.
此外，在收敛到零阶出口压力边界条件时，构造了较易收敛的减缩修正方法。
Furthermore, a reduction correction method is built to promote convergence to boundary condition of exit pressure.
在一合理的假设下证明了该算法具有Q-2阶收敛速率。
The Q-2 order convergence is proved under a reasonable assumption.
给出了同阶差分格式线性组合的性质，从而可设计出更多收敛的多参数曲线细分格式。
Furthermore, the property of the linear combination of the difference schemes of the same order is analyzed, which can help to devise more convergent curve subdivision schemes with several parameters.
由于搜索方向含有目标函数的二阶信息，提高了算法的收敛速度。
With the two degrees information of the object function in search direction, the algorithm improved the convergence.
给出了一种新的求解非线性方程的迭代方法，该算法至少是5阶收敛且不用计算导数，具有收敛速度快，计算精度高的特点。
In this paper we present a new iteration method with high accuracy for solving nonlinear equations, this method has not only 5-order convergence but also avoids the operation of derivatives.
与一般有限元相比可以提高一阶收敛精度，应力可直接在单元节点上得到。
Compared with the general finite element, the present element may have heigher first order convergence rate, the stresses can be obtained at nodes of element directly.
分析了幂数级函数阶数M与其收敛性的关系。
The relationship between the order M of the exponential series function and astringency was also analyzed.
该算法根据均方偏差的收敛条件，在迭代过程中不断减小投影阶数。
According to the condition of convergence on the Mean-Square Deviation, the algorithm decreases its order as iteration goes on.
使用高斯消无法时，该方法可大大降低行列式的阶； 使用SOR法时，该方法可加快收敛速度。
The techniques we employ here greatly reduce solution space of Gaussian method or accelerate convergence of SOR.
为改进网络学习效率及大范围收敛性，提出了网络权值学习的单调同伦方法，该方法具有与牛顿法相同的二阶收敛性。
To improve the learning efficiency and global convergence we present the monotone homotopy method, which has the same convergence as the Newton's method, to train the weights of the network.
利用本文方法所获得的解，无论是位移还是内力可同时有二阶收敛精度。
The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed.
第二章中，给出了一类二阶拟线性方程广义有限元解的渐近展式和超收敛结果。
In chapter two, the asymptotic expansion and superconvergence result of a class of second order quasilinear equation in generalized finite element space is presented.
本文在广义函数的有限阶收敛下，证明等同是一对一的。
This paper proves that the equated concept is One-to-One in the finite order convergence of distributions.
研究了几类K阶整系数线性微分方程解的超级、零点收敛指数和零点超收敛指数，得到一些精确的结果。
The hyper order, the exponent of convergence and the hyper-exponent of convergence of zeros of solutions for some types of K-order linear differential equations with entire coefficients are discussed.
研究了几类K阶整系数线性微分方程解的超级、零点收敛指数和零点超收敛指数，得到一些精确的结果。
The hyper order, the exponent of convergence and the hyper-exponent of convergence of zeros of solutions for some types of K-order linear differential equations with entire coefficients are discussed.
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