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1.
一类求解分片延迟微分方程的线性多步法的散逸性   总被引:12,自引:0,他引:12       下载免费PDF全文
本文研究分片延迟微分方程本身及数值方法的散逸性问题.给出了一个关于此类问题本身散逸性的充分条件,同时得到了一类求解此类问题的线性多步法的数值散逸性结果,此结果表明所考虑的数值方法继承了方程本身的散逸性.数值试验进一步验证了理论结果的正确性.  相似文献
2.
证券组合投资的多目标区间数线性规划模型   总被引:9,自引:0,他引:9  
本文提出了证券组合投资的多目标区间数线性规划模型,引入了收益——风险偏好参数和优化水平参数。投资者可以根据对风险的喜好程度和金融市场的客观情况,适当估计这两个参数,从而得到相应情况下的有效投资方案,使投资过程更具柔性,而且更接近于实际情况。  相似文献
3.
Given an undirected graph G=(V,E) with |V|=n and an integer k between 0 and n, the maximization graph partition (MAX-GP) problem is to determine a subset SV of k nodes such that an objective function w(S) is maximized. The MAX-GP problem can be formulated as a binary quadratic program and it is NP-hard. Semidefinite programming (SDP) relaxations of such quadratic programs have been used to design approximation algorithms with guaranteed performance ratios for various MAX-GP problems. Based on several earlier results, we present an improved rounding method using an SDP relaxation, and establish improved approximation ratios for several MAX-GP problems, including Dense-Subgraph, Max-Cut, Max-Not-Cut, and Max-Vertex-Cover. Received: March 10, 2000 / Accepted: July 13, 2001?Published online February 14, 2002  相似文献
4.
杨柳  陈艳萍 《计算数学》2008,30(4):388-396
本文提出了求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法,即μk=ακ(θ||F_k|| (1-θ)||J_k~TF_k||),θ∈[0,1],其中ακ利用信赖域技巧来修正.在不必假设雅可比矩阵非奇异的局部误差界条件下,证明了该算法是全局收敛和局部二次收敛的.数值试验表明该算法能有效地求解奇异非线性方程组问题.  相似文献
5.
A Conic Trust-Region Method for Nonlinearly Constrained Optimization   总被引:5,自引:0,他引:5  
Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.  相似文献
6.
孙杜杜  舒适 《计算数学》2005,27(1):101-112
本文针对带有间断系数的三维椭圆问题,讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法.通过分析线性和高次有限元空间之间的关系,我们给出了一种新的网格粗化算法和构造提升算子的代数途径.进一步,我们还对新的代数多重网格法给出了收敛性分析.数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。  相似文献
7.
Based on a comparison principle, we discuss the existence, uniqueness and asymptotic behaviour of various boundary blow-up solutions, for a class of quasilinear elliptic equations, which are then used to obtain a rather complete understanding of some quasilinear elliptic problems on a bounded domain or over the entireR N .  相似文献
8.
变分与无限维系统的高精度辛格式   总被引:4,自引:0,他引:4       下载免费PDF全文
王雨顺  秦孟兆 《计算数学》2002,24(4):431-436
1.引 言 冯康和他的研究小组提出的生成函数法[1]系统地解决了象二体问题这样地有限维Hamil-ton系统辛算法的构造问题,该方法也可以自然地推广到无限维Hamilton系统[2].首先在空间方向进行离散,例如采用差分或谱离散,得到有限维Hamilton系统,然后再采用生成函数法离散该系统.这样得到的辛格式是整个一层的格式,对于研究格式的局部性质如多辛性质[3],局部能量守恒性质[5]就相当困难.  相似文献
9.
In this paper, we propose a modified Bregman-function-based proximal point algorithm for solving variational inequality problems. The algorithm adopts a similar constructive approximate criterion as the one developed by Solodov and Svaiter (Set Valued Analysis 7 (1999) 323) for solving the classical proximal subproblems. Under some suitable conditions, we can get an approximate solution satisfying the accuracy criterion via a single Newton-type step. We obtain the Fejér monotonicity to solutions of VIP for paramonotone operators. Some preliminary computational results are also reported to illustrate the method.  相似文献
10.
The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the objective function is bounded below and its gradient is Lipschitz continuous, we prove that (a) any trajectory of the gradient-based neural network converges to an equilibrium point, and (b) the Lyapunov stability is equivalent to the asymptotical stability in the gradient-based neural networks. For a convex optimization problem, under the same assumptions, we show that any trajectory of gradient-based neural networks will converge to an asymptotically stable equilibrium point of the neural networks. For a general nonlinear objective function, we propose a refined gradient-based neural network, whose trajectory with any arbitrary initial point will converge to an equilibrium point, which satisfies the second order necessary optimality conditions for optimization problems. Promising simulation results of a refined gradient-based neural network on some problems are also reported.  相似文献
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