查询词典 limit in the sense of pointwise convergence

In conclusion that there is one and only one balance convergence point is proved and convergence error equation is given when convergence condition is satisfied.

对算法收敛性进行分析和证明，给出算法的收敛判据并证明当满足收敛条件时必存在唯一平衡收敛点，同时给出收敛误差方程。

And change in international convergence from formal convergence to essential convergence.

国际趋同——由重形式趋同向重实质趋同转变。

A strict proof of the formulas of the convergence real part,absolutely convergence part and uniform convergence real part for the exponential series has been given.

给出了指数级数收敛实部、绝对收敛实部及一致收敛实部公式的严格证明。

This includes function of uniform convergence, function series and the uniform convergence of parameter improper integral. We uniform convergence.

这包括函数列的一致收敛，函数项级数的一致收敛以及含参量反常积分的一致收敛。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods , and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search.At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.

本文首先介绍了Newton型迭代法的基础知识，然后着重介绍了B-可微方程的Newton法，给出B-可微法的局部收敛结论，推广了古典的Newton法，但由于收敛的局部性，该算法仍有一定的不足之处；文章在证明大范围收敛定理时，假设M是不可约对角优势矩阵，采用一维Newton寻查的方法，保证算法的收敛性。

For the linear problem, the linearity of the problem is also well preserved in the merit functions. The global convergence, local superlinear or quadratic convergence and finite convergence for linear problems of the proposed algorithms are also obtained under conditions as above or even weaker.

基此构造的互补和混合互补问题的算法，均具备在前述条件或比其更弱条件下的全局收敛性、局部超线性或二次收敛率以及在线性情形下的有限步收敛性。

Experiment in this paper validates the convergence of the improved Mean Shift algorithm, contrast convergence rate of improved Mean Shift algorithm with convergence rate of traditional Mean Shift algorithm.

本文的实验也进一步验证了改进的Mean Shift算法的收敛性，并对比了改进前后的Mean Shift算法的收敛速度。

In this paper, the imprecise proofs existing in some literatures are firstly pointed out. Then, the local convergence is proved in a new way and the condition of convergence to the local maximum point is offered. Finally, the geometrical counterexamples are provided for explanation about convergence of Mean Shift and the conclusion is further discussed.

首先指出了Comaniciu和李乡儒的证明过程存在错误；然后，从数学上重新证明了Mean Shift算法的局部收敛性，并指出其收敛到局部极大值的条件；最后，从几何上举反例分析了Mean Shift的收敛性，并进行了深入比较和讨论。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。