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- The descending property of Newton method has discussed and an example ha. 本文讨论了牛顿法的下降性并给出了算法及计算实例。
- Newton method is adopted and the reactive flash process of MTBE synthesis has been studied as a numerical example. 以含有惰性组分的MTBE反应闪蒸过程为例，用非反应闪蒸方法进行计算，得到了关于反应闪蒸的一般结论。
- Under the assumptions of semismoothness, the global superlinear convergence of the smoothing Newton method was proved. 在半光滑假设条件下，证明了光滑化牛顿法具有全局超线性收敛性。
- In the paper we study the relationship between Davidson method and Newton method and emphasize on studying the inexact Newton method. 本文研究了Davidson方法与Newton方法的关系，并重点研究不精确Newton方法。
- An other way is first to reformulate CPs as a system of nonlinear smooth equations with smoothing parameters, then use the classical Newton method. 这些方法的共同特点是首先将原问题转化为确定(非光滑或带参数的光滑)方程组求解,然后利用非线性方程组的(广义)Newton法思想构造算法。
- Based on [2], [3], [5], [6] and [7], we generalize the classic bisection method to interval space, and replace interval Newton method. 本文在[2]，[3]，[5]，[6] 和[7] 的基础上，先将经典的二分法推广到区间二分法，并用它代替了计算量较大的区间牛顿法。
- Based on the reformulation as a system of nonsmooth equations, a generalized Newton method for solving this system is proposed. 在将原问题转化为一个非光滑方程组的基础上，提出了解此方程组的广义牛顿方法。
- The Newton method with the new gradient is combined with the interior penalty method to obtain the capacitated network flow solution. 利用新梯度的特征，并结合惩罚函数方法，可以获得容量制约下的交通网络流的解。
- At last,based on Lippman-Schwinger integral equation,the newton method is used to solve the reconstruction of the refractive index. 在Lippman-Schwinger积分方程的基础上，用Newton法反演了折射率。
- The objective function in the unconstrained model of linear Support Vector Machine（SVM） is not twice differentiable which precludes the use of a fast Newton method. 摘要 线性支持向量机的无约束优化模型的目标函数不是一个二阶可微函数，因此不能应用一些快速牛顿算法来求解。
- A smoothing function which can be approximated by NCP-function is given and the smoothing Newton method is applied to resolve this nonsmooth operator equation. 构造一个光滑化函数逼近NCP-函数，利用光滑化牛顿法求解此非光滑算子方程。
- The modules of the engine system are calculated iteratively in a predetermined sequence,and a modified Newton method is used to find the unknown variables of the system. 该方法按照预定的计算顺序，对发动机系统的各个模块进行迭代计算，并采用拟牛顿法求解系统可调变量。
- The searching direction is created in the subspace with Newton method which takes advantage of Newton method's fast rate of local convergence while it can avoid too much memory. 通过在较小的子空间内利用牛顿法迭代生成寻优方向，避免了牛顿法的存储困难又发挥了它的快速收敛性。
- Sui Yunkang and Yang Zhiguang, Modified Newton Method and Dual Method through a Rational Approximation at Two Expanded Points ,Engineering Optimization, Vol.24 (1995 ): 1-17. 隋允康，结构优化的曲线寻优理论及其逼近论和常微分方程组解法，中国学术期刊文摘，1卷2期(1995).
- On the basis of this reformulation, it is proved that the system of nonsmooth equations is strongly semismooth so that the generalized Newton method for solving this system possesses locally quadratic convergence. 在此基础上，证明了非光滑方程是强半光滑的，因而解此方程的广义牛顿法具有局部二次收敛性。
- Secondly, we absorb the preconditioning idea of Davidson method and preconditioned Lanczos method and propose preconditioned inexact Newton method and preconditioned block inexact Newton method. 其次借鉴Davidson方法和预处理Lanczos方法的预处理思想，提出了预处理不精确Newton方法和预处理块不精确Newton方法。
- Davidson method and Newton method are two effective methods for computing the extreme eigenvalues of symmetric matrices. Davidson方法和Newton方法是求解对称矩阵特征值的两种有效方法。
- In our study, a new kind of Newton-PCG like algorithms is derived and it is proved that they are superior to the exact Newton method by the theoretical analysis and numerical experiments. 本项目针对一般的无约束优化问题，研究这类算法的有效性的定量指标，并构造出理论上确保更为有效的算法，将该算法同牛顿法作了比较。
- The method seems good but it needs to be tried out. 这个方法似乎不错，但需要试验一下。
- Switched capacity circuit structures of gradient methods are proposed,the common properties of the steepest descent method, Newton method and quas Newton methods are analysed. 建立了梯度法的开关电容电路结构，分析了最速下降法、牛顿方法和拟牛顿法的共同特点，研究无约束差分优化的开关电容电路结构。
