迭代的

The numerical ex-periment has shown that the number of iterations depends significantly on the positiveparameterα,β. But, in general, it is di?cult to choose a proper parameterα,β. Thuswe propose new self-adaptive alternating direction method which adjusts the scale pa-rameter automatically per iteration based on the message of the iterates. We have provedthe convergence of the method under mild assumptions.Finally, we present some numerical results.

对于我们提出的新交替方向法，数值实验表明，迭代的步数与时间与所取的参数α，β有关，然而我们很难去选择一个合适的参数α，β，因此我们提出新自适应交替方向法，对其中的参数α，β进行自适应调整，这种自适应算法根据每步迭代信息自动地调整参数α，β，并证明了算法的收敛性。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

An iterative factorization method based on linear subspace for projective reconstruction is presented in the paper. It relies on the facts that the rows in the matrix including all the image points span the same linear subspace as the rows in the matrix including space points and the fact that any basis of the subspace can be regarded as projective reconstruction. The projective reconstruction and the depth factors are obtained based on linear iteration.

摘要该文提出了一种基于子空间线性迭代的射影重建方法，该方法利用所有的图像序列构成的行向量生成的线性子空间之和与射影重建结构点构成的行向量生成的子空间是同一线性子空间及在该子空间中任何一个基底都可以作为射影重建的特性，线性迭代地求取射影重建及图像深度因子。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

With complex analytical analysis for B, the fixed points of B at real axis and C-plane are found. It is proved that zero is the only attract fixed point and the iteration of B on the complex plane is symmetrical. And the domains of the constringency and the divergence of B are given.

通过对B的复解析分析，得出了B在实轴和复平面上不动点的性质与求解方法，证明了0点为唯一的吸引不动点；说明了B在复平面上迭代的对称性，求出了函数迭代在整数点处的敛散区域。

By the iterative functional equation we usually mean an equation containing at leastan n-th iterate〓of an unknown function.A relatively general form of it is〓(1)where〓is a given integer,J is a connected closed subset of the real number axis R,G is a given〓function from〓to R,and f is an unknown function to be solved.

迭代函数方程通常是指含有未知的函数并含有它的至少2次迭代的方程，它的一个比较广泛的形式是〓，对任〓，（1）其中〓是个给定的整数，J是实数轴R的一个连通闭子集，G是个给定从〓到R的〓映射，f是个未知而待求的函数。

That the generation of smaller candidate sets enables us to effectively trim the transaction database size at a much earlier stage of the iterations, thereby reducing the computational cost for later iterations significantly.

要注意，生成较小的候选集可以使我们在迭代的早期有效地削减事务数据库的大小，从而大大地减少了以后的迭代的计算量。

The inclusion cell is the bridge of macro and micro mechanical-electrical responses, but also provides a direct relationship between meso/micro grain characteristic parameters and between globe macro performance, which could become a great help for the study on damage, fatigue and fracture mechanism of ferro-electrics.

通过采用基于Hill理论的扩展的自洽计算方法，将其从一般多晶材料、复合材料的纯力学性能描述，扩展到具有力电耦合的复杂情况，建立其整体迭代和局部迭代的计算方法，得到铁电多晶材料的非线性力电耦合关系的描述。

The solution of the optimal 3-impulse rendezvous is a multi-variable iteration process. For the 3-impulse rendezvous with terminal coastings, the symmetry characteristic of optimal 4-impulse rendezvous was applied to reduce the number of the iteration variables to save the calculation consumption.

三脉冲最优解的求解采用多变量迭代的方法；对于存在端点滑行段的三脉冲最优解的求解，利用四脉冲最优解的对称性，减少迭代变量的数量，降低了计算量。

The position equations are non-linear and they are very difficult to be solved. Scholar Haworth, et al. presented an iterative algorithm.

学者Haworth等人(1995，1997)提出了利用迭代的算法求解；然而该文的实验结果表明Haworth等人的迭代算法是发散的。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。