收敛

From the matrix theory and the general principle of the iterative convergence of the linear coupled equations, this dissertation firstly proved the sufficient necessary convergent conditions for CMAC batch learning as well as the necessary convergent conditions for CMAC incremental learning, in which no additive conditions were needed. The past researchers'conclusions under the special condition of the positive articulation matrix are generalized and improved.

从矩阵理论和线性方程组迭代收敛的一般性原理出发，首次在不附加特殊条件的情况下，证明了CMAC学习算法在批量和增量两种学习方式下收敛的一般性定理，给出CMAC算法在批量学习方式下收敛的充要条件，以及在增量学习方式下收敛的必要条件，对前人在关联矩阵正定的特殊条件下得出的结论进行了推广和改进。

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

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

They didn't possess strong convergence and quadratic convergence rate,more-over,their convergence properties and rate of convergence were only local.

无强收敛性和二次收敛率，甚至收敛性与收敛速度只是局部的。

Under weaker conditions without the strict com-plementarity,the new algorithm still possesses global convergence,strong convergence,superlinearconvergence and quadratic convergence rate.

在无严格互补的条件下，仍获得算法的全局收敛性、强收敛性、超线性收敛性及二次收敛速度。

This method takes the advantages of fast convergence of CG and not easily to trap the local extreme of SH, which make it can converge to global extreme at a high rate of speed in solving the problems of quadratic function optimization.

这种方法结合了共轭梯度法的快速收敛和随机爬山法的全局收敛的优点，在求解二次函数极值的问题上具有收敛速度快，并能收敛到全局极值的特点。

Then, the convergence and convergence rate of three kinds of GA above are analyzed comprehensively from the point of view of stochastic matrix and matrix eigenvalue. The general convergence analysis methods of GA by Markov chains are presented and the convergence rates are discussed emphatically.

然后，利用有限Markov链从随机矩阵和矩阵特征值两个角度全面分析了上述三种类型GA的收敛性和收敛速度，给出了利用Markov链分析GA收敛性的通用方法，重点讨论了它们的收敛速度问题。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

Our results show that not only the club convergence has been obviously exhibited, that is, the output per capita congregates within the east, middle and west districts respectively; but also the conditional convergence has been identified, that is, given the same level of human capital, market ope...

本文认为中国地区间的经济增长，不仅存在着显著的&俱乐部收敛&特征，即按东中西划分的区域内部人均产出具有明显的聚集现象；而且存在着条件收敛的特征，即在具有相同的人力资本、市场开放度等结构特征的经济地区间存在着一定的增长收敛趋势。本文实证分析的结果还显示，各地区间工业化水平的差异和产业结构的变动对增长收敛性构成显著的影响。

A general equation was derived for calculating the coordinates of the convergent point. The physical meaning of the coordinates was discussed from the point of view of thermodynamics. The ordinates of the two kinds of convergence are the same, i.e. the free energy change of the solutes is equal to zero.

建立了溶质平均收敛点坐标的计算方程，并从自由能变的角度表征了收敛点坐标的物理意义，阐明了收敛点的纵坐标相等的原因是溶质在收敛点处的自由能变为零。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。