收敛的阶

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

Furthermore, it is shown that the design of the ar- bitrary matrix plays an important role in the enlarging the domain of attraction and then improving the convergence of UKF significantly.

基于UT的二阶或者三阶逼近，我们研究了算法收敛的充分条件，并进一步证明了如何选取合适的矩阵来提高UKF算法的收敛性。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

Based on the analysis of some aspects, such as the approximative algorithm of FOC, the Tustin transform theory and its generating function formula's character, the convergence guarantee of binomial power function by Maclaurin expanding, and the consideration of the limitation of conventional methods, an improved method is proposed to compute the numerical evalution of FOC using PSE and Tustin transform and is further applied to solving the linear FOS.

以分数阶算子近似方法的分析研究为基础，基于Tustin变换理论及其用于分数阶算子的离散生成函数公式特点，利用二项式幂函数的Maclaurin展开能够保证收敛的特性，考虑常用算法的局限性，提出了一种改进的基于幂级数展开和Tustin变换的分数阶运算方法，并应用于线性分数阶系统的求解，给出了递推算法的详细推导。

To obtain quadratical convergence, however, strict complementarity condition at the Danskin point was used. The condition is too strict to be satisfied in many practical problems such as discrete semi-infinite minimax problem. Another kind of Newton method for finite minimax problems was presented by E. Polak and, without strict complementarity at the Danskin point, superlinear convergence (of order 3/2) was proven.

Polak等人提出了一种直接求解极大极小问题的二阶收敛的牛顿法，但是为获得二阶收敛速度要求在Danskin点处满足严格互补条件，这个条件太强，很多实际问题尤其是半无限极大极小问题的离散化不满足该条件；他们又给出另外一种牛顿法，在不假设严格互补条件成立的情况下，证明了它的超线性（3/2阶）收敛性。

The necessary and sufficient conditions for convergent of characteristic domain and the conditions for tangent plane continuity are obtained. The conditions for having limited value of the second order of differential at the convergent point are shown as well.

给出了任一特征域收敛的充要条件；给出了曲面在任一极限收敛点上达到一阶几何连续的条件；分析了极限收敛点处的二阶连续，给出了二阶导数有界的条件。

This scheme, by a rigorous analysis, is proved to be unconditionally stable and convergent, its global error order is also obtained.

经过严格的理论分析，证明了该差分格式是唯一可解的、无条件稳定的和收敛的，并给出了收敛阶。

Using the asymptotically compact theory of Anselone' and Stepleman' theorem, the existence, the unicity , the convergence and the error estimate with O(h3) of the discrete equations are shown....

并借助Anselone的渐近紧收敛理论和Stepleman定理，证明了离散方程组的解存在性、唯一性、收敛性和精度阶O(h~3)。使用Ostrowski的不动点定理，提供了三阶收敛的迭代法。

It is proved that Newton iteration method is still quadratically convergent under a weak condition, and a new point is added to Newton s method , i.

本文讨论求解非线性方程的牛顿法，证明牛顿法在一个弱条件下仍保持局部二阶收敛性，给出牛顿法的一点改进，即一个不带导数的单参数的二阶收敛的迭代法，而且分别得到这两种迭代法的收敛因子，最后进行数值实验

We show that the hybrid method is globally and superlinearly convergent for nonzero residual problems and globally and quadratically for zero residual problems.

因此，该杂交方法对于零残量问题是二阶收敛的，而对于非零残量问题是超线性收敛的。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。