共查询到19条相似文献,搜索用时 93 毫秒
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1引言考虑非线性互补问题NCP(f):的求解,即我们要寻求某x∈Rn,使其满足(1.1).其中映射f:Rn→Rn为具有连续F-导数的非线性映射.众所周知,问题(1.l)可以等价地转化为B-可微方程组:求解,其中:容易证明,由(1.3)定义的映射G处处B-可微,且其在点x∈Rn处的B-导数BG(x)为而对于问题(1.2)(1.3),我们希望直接用经典的广义Newton法进行求解.但是,由于由(1.3)定义映射G在(1.1)的解x∈Rn处,没有可逆的强F-导数存在,因此,关于算法(1.5)(1.6)… 相似文献
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1引言设R~n.R_+n.R_+~n分别表示Euclidean空间及R~n的非负和正子空间:符号┃·┃表示向量或矩阵的2-范数,非线性互补问题(NLCP) 相似文献
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本文讨论了多重分裂算法在求解一类非线性方程组的全局收敛性和单侧收敛性.当用研步Newton法来代替求得每个非线性多重分裂子问题的近似解时,同样给出相应收敛性结论.数值算例证实了算法的有效性. 相似文献
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本文将解线性方程组的AOR迭代法推广到解非线性方程组,构造和研究了Newton-AOR方法,建立了收敛性定理和比较定理,在一定条件下,从理论上证明了Newton—AOR方法比Newton—SOR方法收敛快,并给出了数值例子。文中所用有关概念和记号的意义见[1]。 相似文献
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本文对于Johnson、Austria提出的求解非线性方程组的基于矩阵三角分解修正的一类拟Newton法进行了改形,并给出了该算法的Kantorovich型的收敛性分析,从而完整了文(l]的收敛理论,亦为算法的初始选取,提供了依据. 相似文献
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本文研究由双障碍问题导出的一类B可微函数的性质,并在一定条件下证明了求解相应的B可微方程阻尼牛顿法的全局收效性和二阶收效性.数值例子表明这一算法是有效的. 相似文献
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Newton法及其各种变形收敛性的统一判定法则 总被引:11,自引:1,他引:10
1引言Banach空间中的算子方程是非常广泛的应用数学课题,而求方程数值解的主要方法是Newton法及其各种变形.自从Kantorovich关于Newton法收敛性的著名定理建立以来,有大量的文献在种种相仿的条件下研究各种变形收敛性的各种判定法则.在此,本文建立了统一的判定法则.首先,把Kantorovich算子类K(1)(x0,y)扩充为K(1)(x0,y,C),并给出类K(1)(x0,y,C)的扩类Kcent(1)(x0,y,C)和子类K(2)(x0,y,C).对于这些算子类,确定了一个仅依… 相似文献
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We present a generalized numerical embedding algorthm for solving nonsmooth equations based on the results in [1],COnvergence of the algorithm is proved carefully and implementation is discussed.Application of the algorithm to the complementartity problem,Variational inequalities and nonlinear optimization problemis discussed. 相似文献
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ON THE CONVERGENCE OF PARALLEL BFGS METHOD 总被引:1,自引:0,他引:1
ONTHECONVERGENCEOFPARALLELBFGSMETHODChenZhongFeiPusheng(DepartmentofMathematics,WuhanUniversity,Wuhan430072,China.)ZhouYuncai... 相似文献
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A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals. 相似文献
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A semilocal convergence theorem is given for Newton method solving complementarity problems, which is identical in form to the standard Kantorovich theorem. All the convergence condition can be verified computationally. 相似文献
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GLOBALLY CONVERGENT INEXACT GENERALIZED NEWTON METHODS WITH DECREASING NORM OF THE GRADIENT 总被引:1,自引:0,他引:1
Ding-guo Pu 《计算数学(英文版)》2002,20(3):289-300
AbstractIn this paper, motivated by the Martinez and Qi methods[l], we propose one type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems in which the objective functions are not twice differentiable, but have LC gradient. They make the norm of the gradient decreasing. These methods are implementable and globally convergent. We prove that the algorithms have superlinear convergence rates under some mile conditions.The methods may also be used to solve nonsmooth equations. 相似文献
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1 IntroductionIn this paper,we firstprovide a generalized difference method for the two-dimension-al Navier-Stokes equations by combining the ideas of staggered scheme[6] and generalizedupwind scheme [4 ] in space,and by backward Euler time-stepping.Then we apply theabstractframework of[7] to prove its long-time convergence.The outline of this paper is as follows:In§ 2 we state the generalized differencemethod.In§ 3 we provide some lemmas.In§ 4 we study the one-sided Lipschitz condi-tio… 相似文献
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§1.前言 设X和Y是Banach空间,p(x)是定义在区域G X上并取值于Y的非线性算子。假定p(x)有Frechet导算子p’(x),为了近似解算子方程 p(x)=0, (1)研究了如下的迭代程序: x_(n 1)=x_n-A_np(x_n), A_(n 1)=2A_n-A_np(x_(n 1)A_n,(2)这里x_0∈G和A_0∈(Y→X)都是初始近似,其中x_0是方程(1)的近似解,而A_0则是p(x_0)的近似过算子。[1]在一些条件下证明了程序(2)收敛于方程(1)的解。 相似文献