查询词典 convergence behavior

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

As for the optimization problem, the damped Gauss-Newton Method algorithm is employed for obtaining its solution, and analysis the global convergence of the algorithm, also, the superlinear convergence rate and two order convergence rate of the algorithm is given.

对该优化问题，我们用阻尼高斯牛顿算法求解，并对算法的全局收敛性和超线性收敛速度进行了分析。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

The projection gradient method will be a possible way to solve the problem that we just get. It has been shown that the projections of the every directions, of which is the boundary point in linear restraint problems, are the possible decent directions, and the projection of negative grads direction is a decent direction. In 1960, Rosen proposed the basic idea of projection gradient methods, and then lots of researchers have been tried to find the convergence of this method. But most of them get the convergence with the condition to amend the convergence itself.

在约束最优化问题的算法中怎样寻找有效的下降方向是构造算法的重要内容，在寻找下降方向方面可行方向法中的投影梯度法有效的解决了下降方向的寻找问题，利用线性约束问题边界点的任意方向在边界上的投影都是可行方向，而负梯度方向的投影就是一个下降方向。60年代初Rosen提出投影梯度法的基本思想，自从Rosen提出该方法以后，对它的收敛性问题不少人进行了研究，但一般都是对算法作出某些修正后才能证明其收敛的，直到最近对Rosen算法本身的收敛性的证明才予以解决。

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。

First,we proposes the acceleration of Monte Carlo EM Algorithm,which is based on Monte Carlo EM Algorithm and Newton-Raphson algorithm,to improve the convergence rate;Second,the it is shown that the accelerated EM algorithm we proposed has quadratic convergence rate in a neighborhood of the posterior mode;Finally,its excellent performance in convergence rate is illustrated by a classical example.

受Monte Carlo EM算法与EM加速算法启发，本文构造了一种新的EM算法，称为Monte Carlo EM加速算法；证明了该算法在似然函数/后验分布的众数的附近确实具有二次收敛速度，改进了Monte Carlo EM算法的收敛速度；并通过一个数值例子的计算结果说明了该算法的优良性，它兼具实现简单及收敛速度快的特点。

On this basis, according to historical data, apply ANN and differential simulation method to get the quantitatively correlative relations between each production and its own influence factors, and introduce the new methods of prediction for dynamic indexes with gas-field development (The combinatorial prediction method based on fuzzy comprehensive evaluation, the method of ANN to select optimally combinatorial prediction models and the ANN prediction method based on genetic algorithm).(2) Base on mathematical programming, combine with quantitative economics and techno-economics, introduce economical indexes to establish production"s distribution optimal model, production"s constitution optimal model and measured production"s constitution optimal model, including multi-objective models and five-years models. Upon this, the optimal project for all gas field and each gas-collected factory can be got. Also, introduce the time value of capitals to improve on these models.(3) Base on the optimal solution theory and algorithm theory for the nonlinear programming problem, introduce the SUMT algorithm and genetic algorithm to study how to solve the models, and on the basis of normal genetic algorithm, make use of auto-adaptively modulating method to improve on normal genetic algorithm; Base on algorithm"s convergence theory and calculation"s complexity theory to analyze seriatim SUMT algorithm"s convergence and genetic algorithms convergence, and compare performance with each other.

在此基础上，利用神经网络方法和微分模拟方法根据历史数据得到各分项产量与其影响因素之间的定量关联关系，并引入气田开发动态指标新的预测方法(基于模糊综合评判的组合预测方法、神经网络优选组合预测模型预测方法以及基于遗传优化的神经网络预测方法)；(2)以数学规划为基础，结合数量经济学和技术经济学，引入经济指标建立产量分配优化模型、产量构成优化模型、措施产量构成优化模型、气田开发多目标规划模型以及五年规划模型，进而获得全气田及各采气厂的最优方案，并引入资金时间价值对五年规划模型进行改进；(3)以非线性规划问题的最优解及算法理论为基础，引入SUMT算法以及遗传算法对模型的求解进行研究，并在原有的遗传算法基础上，引入自适应调整方法对遗传算法进行改进；以算法的收敛性理论和计算复杂性理论为基础，逐一分析SUMT算法以及遗传算法的收敛性，并比较三种算法的优劣性。

Simulation shows that MSA has strong robustness, good global convergence, quick convergence speed and high convergence accuracy.

仿真结果证明：MSA鲁棒性较强，全局收敛性好，收敛速度较快，收敛精度较高。

Chapter 2 investigates the convergence of triple and n -ple Dirichlet series, the convergence of triple random Dirichlet series under certain conditions, and the convergence of double bi-random Dirichlet series under the conditionand obtains some results similar to double Dirichlet series.

此外还在条件 sum from m=1 to +∞ sum from n=0 to +∞ P{|X_|≥m~pn~p}＜+∞下，研究了二重双随机Dirichlet级数的收敛性，得到了一些类似于二重Dirichlet级数的有关结论。

This paper first gives a continuous function, convergence, uniform convergence of function series, such as the definition of the concept, let us on the continuity and with the convergence of the initial understanding.

摘 要：本文首先给出函数连续性、收敛性、函数项级数一致收敛等概念的定义，让我们对连续性与收敛性有了初步的了解。

According to our present broadcasting situation,the thesis proposes using new technology to update and reform the present HFC. It also suggests broadcasting using self-advantage and arranging EPON in order to win the supermarket.

论文从我国广电的现状出发，结合实际，积极倡导采用新技术更新、改造我国现有的HFC网络；倡导广电现阶段利用自身优势，部署EPON网络来赢取市场。

A new general kinetic equation was derived in which the effect of the removal of condensation water was taken into account completely, and was applied to the polyesterification kinetic study of AA/HPHP and AA/NPG. It was found that the reaction order of self-catalyzed polyesterification was not constant. For these polyesterifications, the reaction order was 2.5 at a low temperature, while 3.0 at a high temperature.

考虑缩合水的排除对反应体系的影响，用体积浓度单位推导出一个新的聚酯反应总包动力学方程，并应用到AA/HPHP和AA/NPG两个聚酯化反应的动力学研究中，研究发现，自催化聚酯反应的反应级数并不是固定值，对于AA/HPHP和AA/NPG两个聚酯化反应而言，低温时反应级数为2.5，高温时反应级数为3.0。