查询词典 iterative method for eigenvalue problems

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。

The unified discrete iterative map model of peak current and valley current controlled buck, boost, and buck-boost converters is established, and the unified piecewise smooth iterative map and their corresponding characteristics equations are also derived.

本文建立了峰值电流和谷值电流控制Buck，Boost，及Buck-Boost变换器的统一离散迭代映射模型，并导出了统一的分段光滑迭代映射方程及特征值方程，通过数值仿真得到了占空比变化时的正、逆分岔图和Lyapunov指数谱。

This paper presents a stability criterion for design iterative learning controller. From the criterion,one can change the design problem into finding a positive definite discrete matrix kernel. It has been shown that what kind of variable can be controlled by the iterative learning,(2) and what kind of filter can be included into the controller.

摘要提出了一种针对自学习控制的稳定性判据，应用这一稳定性判据将自学习控制器的设计转化为寻找正定离散矩阵核，从而回答了两个问题，其一什么样的量可以通过自学习叠代加以控制，其二学习叠代中什么样的滤波环节的引入不会影响学习收敛性。

We analyzed the main factors that influence on the quality of reconstruction image. These factors are filter function, projection data, sampling space and noise level in filter backprojection, and the choice of relaxation parameter, the fashion of data access, the choice of basis function and the estimate of optimum iterative times in algebra iterative algorithm.

详细分析了影响滤波反投影算法图像重建质量的基本因素(滤波函数的选取，投影数，抽样间距，噪音的大小)和代数重建算法图像重建质量的几个因素(松弛引子的选择，数据访问方式，基函数的选择，最优迭代次数的估计)。

An iterative algorithm for a class of set- value d mixed variational inequalities is presented by means of resolvent operators of set- value d mappings, and the convergence of the iterative algorithm is discussed.

摘要利用集值映射的预解算子，提出了求解一类集值混合变分不等式问题的迭代算法，并讨论了该算法的收敛性，推广了已有文献的结果。

In chapter 2, for the iterative matrix M~(-1)N in solving linear system, upper bounds of the spectral radius of some iterative matrix are discussed.

第二章针对迭代求解线性方程组中的迭代矩阵M~(-1)N，讨论了其谱半径的上界估计。

In SMFSIA/CAG, to increase computational efficiency in solving the matrix equation, both the speed of the iterative convergence and the matrix-vector multiplication are picked up based on iterative theory. The extended formula of the high order Taylor's series about the horizontal distance is derived. The relationship between the Taylor's series or the neighborhood distance and the efficiency of the arithmetic are analyzed.

在SMFSIA/CAG中，基于迭代法的原理，通过加快迭代收敛速度和加速矩阵向量积两个方面对该算法进行了改进，推导了关于平面展开的高阶泰勒级数展开公式，并对近场相关距离和泰勒级数展开阶数对算法效率的影响进行了分析。

The constructing process of the algorithms itself indicate that they are brevity and have definite geometric meaning, scientific iterative terminal criterions and no strict requirement to function. Finally, some digital experimentation is presented to indicate the algorithms application in solving the problem of maximum of function, transcendental equation,integer programming and so on. The results indicate that the algorithms have more global and more adaptability compared to traditional algorithms and have more calculating efficiency and more scientific iterative terminal criterions compared to some present popular artificial intelligence algorithms.

算法的构造过程本身表明了该算法简单明了、几何意义明确、迭代终止准则科学、对函数的要求较低；最后举了几个数值试验的例子以说明该类算法在求函数的最值，解超越方程以及整数规划等问题中的应用；数值试验的结果标明该算法比单纯由"微分"思想演化而来的传统算法有更好的全局性和对问题的更广泛的适应性，比现在流行的一些人工智能方法有更高的运算效率和更适当的迭代中止准则。

In this paper, the effects to image reconstruction by adopting different ways of sequence's truncation in unrelaxed iterative algorithm is discussed and further studying on the conditions to iterative reconstruction with phase -only have been done.

Sh~n在1949年发表了采样定理，提出在一定条件卜，可以用离散采样值重构带限连续信号。七十年代，l铭an等人提出了几个从零交叉点重构带通或带限信号的定理及其算法。1983年J.L.C.Salu和T.S.Huang对各种关于频谱有限信号外推问题的算法进行分析，提出了统一的迭代算法。

In section 3, on the base of the iterative algorithm, we obtain a new iterative algorithm which is convergent to the signal faster than the old one. In section four, if the form of φ is simple and the sampling set is the integer set Z, then a direct reconstruction formula is presented.

在第二节，我们通过计算对偶框架来重建信号，这与传统的计算对偶框架方法不一样，该算法是通过计算一个矩阵的逆矩阵来计算对偶框架，当矩阵是奇异矩阵时，可通过奇异值分解方法或截断奇异值分解算法来求矩阵的广义逆矩阵。

Continuously improve the production mechanism, to provide customers with better quality products and services.

不断的完善生产机制，给客户提供更优质的产品及服务。

B:Yes, he was the very prize-winner in the court tennis ten years ago?

是的，他是十年前的世界网球冠军。