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newton method相关的网络例句

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At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods , and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search.At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.

本文首先介绍了Newton型迭代法的基础知识,然后着重介绍了B-可微方程的Newton法,给出B-可微法的局部收敛结论,推广了古典的Newton法,但由于收敛的局部性,该算法仍有一定的不足之处;文章在证明大范围收敛定理时,假设M是不可约对角优势矩阵,采用一维Newton寻查的方法,保证算法的收敛性。

By using accelerating Aitken method in iterative method of nonlinear equations, a new modified method is given. The method is applied to modified Newton method, thereby a new method is developed, which is faster and stable. Also, its algorithm is given. Numerical results show that the new method is very efficient.

通过对非线性方程组的迭代法引入Aitken加速技术,设计了一种非线性方程组的迭代解法的加速方法;将该方法与M步Newton法相结合,得到一种收敛速度快而且计算稳定的方法,并给出了具体算法;数值结果表明了新算法是有效的。

The paper contains four parts. In the first chapter, the application back ground and the main algorithms of the complementarity problems is introduced. In Chapter 2, some basic definitions and theories of complementarity problems are introduced. The 3rd chapter is the most important part of this paper, in which a modified smoothing Newton method is detailed; also the global convergence is established for the method.

全文共分为四章,各部分内容安排如下:第一章是绪论部分,介绍了互补问题的应用背景和近年来有关互补问题求解方法的研究成果;第二章是预备知识,介绍了与求解互补问题有关的一些定义以及相关的定理和推论;第三章是本文的重点,提出了求解互补问题的一种修正的光滑Newton算法,从理论上对算法的全局收敛性了证明;第四章是这种修正的光滑Newton法用于求解广义非线性互补问题中,同样证明了算法的全局收敛性。

In-exact Newton method, which is based on Newton method, is one of the main methods for solving large sparse systems of nonlinear equations.

在Newton法的基础上发展而得到的不精确Newton法是目前求解大规模稀疏非线性方程组的主要方法之一。

Newton method and its variant m step Newton method are very important and frequently used for solving these problems.

在诸多解法中,Newton迭代法及其变体M步Newton法是最主要、最常用的方法。

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。

According to the primary principles of the half division method and Newton method ,a new method called horizontal secant method was presented for one dimension search.

根据经典的一维搜索算法———对分法和Newton 切线法的基本原理,提出了一种新的一维搜索算法———水平割线法。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论,利用著名的F-B互补函数的光滑形式,首先将互补问题的求解转化为求解一系列光滑的非线性方程组,然后给出了一种修正的光滑Newton法,该方法不仅放宽对函数F的要求,在Newton方程不可解时引入初始效益函数的最速下降方向,而且光滑因子的选择也比较简单可行,同时在适当的条件下,证明了其算法具有全局收敛性;另一方面,借助另一种F-B光滑函数,将多面体锥上的广义互补问题转化为一种光滑形式,讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系,并将这种修正的光滑Newton法用于求解广义非线性互补问题中,在适当的条件下,该算法同样具有全局收敛性。

In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved.

本文导出了一类无记忆非拟 Newton 公式,并证明了采用非精确线搜索的无记忆非拟 Newton算法的全局收敛性。

The existence and convergence theorem of Newton method and quasi Newton method solving nonlinear equation with parameters F = 0 is obtained under point estimates and weak conditions.

在点估计条件下给出用Newton法及拟Newton法求解带参数非线性方程F = 0解的存在性定理和收敛性定理,以及误差估计。

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