共查询到20条相似文献,搜索用时 15 毫秒
1.
Magnus Sv?rd Siddhartha Mishra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,63(6):985-1003
We consider initial-boundary-value problems for systems of conservation laws and design entropy stable finite difference schemes to approximate them. The schemes are shown to be entropy stable for a large class of systems that are equipped with a symmetric splitting, derived from the entropy formulation. Numerical examples for the Euler equations of gas dynamics are presented to illustrate the robust performance of the proposed method. 相似文献
2.
Randall J. Leveque 《纯数学与应用数学通讯》1984,37(4):463-477
A natural generalization of Godunov's method for Courant numbers larger than 1 is obtained by handling interactions between neighboring Riemann problems linearly, i.e., by allowing waves to pass through one another with no change in strength or speed. This method is well defined for arbitrarily large Courant numbers and can be written in conservation form. It follows that if a sequence of approximations converges to a limit u(x,t) as the mesh is refined, then u is a weak solution to the system of conservation laws. For scalar problems the method is total variation diminishing and every sequence contains a convergent subsequence. It is conjectured that in fact every sequence converges to the (unique) entropy solution provided the correct entropy solution is used for each Riemann problem. If the true Riemann solutions are replaced by approximate Riemann solutions which are consistent with the conservation law, then the above convergence results for general systems continue to hold. 相似文献
3.
High-dimensional reliability analysis is still an open challenge in structural reliability community. To address this problem, a new sampling approach, named the good lattice point method based partially stratified sampling is proposed in the fractional moments-based maximum entropy method. In this approach, the original sample space is first partitioned into several orthogonal low-dimensional sample spaces, say 2 and 1 dimensions. Then, the samples in each low-dimensional sample space are generated by the good lattice point method, which are deterministic points and possess the property of large variance reduction. Finally, the samples in the original space can be obtained by randomly pairing the samples in low-dimensions, which may also significantly reduce the variance in high-dimensional cases. Then, this sampling approach is applied to evaluate the low-order fractional moments in the maximum entropy method with the tradeoff of efficiency and accuracy for high-dimensional reliability problems. In this regard, the probability density function of the performance function involving a large number of random inputs can be derived accordingly, where the reliability can be straightforwardly evaluated by a simple integral over the probability density function. Numerical examples are studied to validate the proposed method, which indicate the proposed method is of accuracy and efficiency for high-dimensional reliability analysis. 相似文献
4.
本文构造了求解无约束非线性lp问题的新方法——调节熵函数法。给出了数值算法,证明了算法的收敛性。通过数值仿真将该方法与求解无约束非线性lp问题的极大熵函数法进行了比较,表明该算法是十分有效的。 相似文献
5.
Junxiang Li Jiazhen Huo 《Applied mathematics and computation》2011,218(6):2750-2760
A new algorithm for the solution of large scale minimax problems of a finite number of functions is introduced. The algorithm is a smoothing method based on a maximum entropy function and an inexact Newton-type algorithm for its solution. Under mild assumptions, only the approximate solution of a linear system is required at each iteration. The algorithm is shown to both globally and superlinearly convergent. Meanwhile some implementation techniques taking advantage of the sparsity of the Hessians of the functions and alleviating the disadvantage effect of the ill-conditioned matrix are considered. Numerical results show that the inexact method is considerably efficient. 相似文献
6.
James Baker-Jarvis Dwight Schultz Jihad Alamendine 《Numerical Methods for Partial Differential Equations》1989,5(2):133-142
A technique to approximate the solution to linear and nonlinear boundary value problems is developed and numerical examples are presented. The technique is based on the method of maximum entropy with moments of the differential equation used as constraints. The method is very general and has the advantage that additional information can be fed into the solution, such as the function's domain or the positivity or negativity of the solution. The technique should find applications in approximating solutions to equations which may or may not contain noise and as an alternative to finite difference and Fourier series solutions and may have applications to large scale simulations. 相似文献
7.
李岭 《数学的实践与认识》2014,(8)
提高多目标决策问题评价结果的客观性、准确性,一直是决策科学研究的重要课题.结合熵权、DEA等数学方法对多目标决策问题进行研究,构造混合评价方法.首先通过构造熵权模型,获取主观权重;其次DEA的方法对多目标决策问题进行综合评价,得到问题的综合评价值,最后根据评价结果进行问题分析和判断.算例结果表明,方法能够应用于多目标决策问题,评价结果客观、准确. 相似文献
8.
基于熵权多目标决策的方案评估方法研究 总被引:28,自引:3,他引:25
给出了一种基于熵权多目标决策的方案评估方法.该方法在只有判断矩阵而没有专家权重的情况下,对有多个评价指标的方案评估问题,通过多对象关于多指标的评价矩阵的熵权计算,对多个合理方案进行优选评估,得出了可信度较高的优选方案,并将这一方法应用在航空装备维修费效益评价实例中. 相似文献
9.
The iterative primal-dual method of Bregman for solving linearly constrained convex programming problems, which utilizes nonorthogonal projections onto hyperplanes, is represented in a compact form, and a complete proof of convergence is given for an almost cyclic control of the method. Based on this, a new algorithm for solving interval convex programming problems, i.e., problems of the form minf(x), subject to γ≤Ax≤δ, is proposed. For a certain family of functionsf(x), which includes the norm ∥x∥ and thex logx entropy function, convergence is proved. The present row-action method is particularly suitable for handling problems in which the matrixA is large (or huge) and sparse. 相似文献
10.
一类无约束离散Minimax问题的区间调节熵算法 总被引:3,自引:0,他引:3
LiSubei CaoDexin WangHaijun DengKazhong 《高校应用数学学报(英文版)》2004,19(1):37-43
In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C^1. The paper deals with this problem by means of taking the place of maximum-entropy function with adjustable entropy function. By constructing an interval extension of adjustable entropy function and some region deletion test rules, a new interval algorithm is presented. The relevant properties are proven, The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum-entropy algorithm. Both theoretical and numerical results show that the method is reliable and efficient. 相似文献
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12.
Sven Erlander 《Mathematical Programming》1981,21(1):137-151
This paper treats entropy constrained linear programs from modelling as well as computational aspects. The optimal solutions to linear programs with one additional entropy constraint are expressed in terms of Lagrange-multipliers. Conditions for uniqueness are given. Sensitivity and duality are studied. The Newton—Kantorovich method is used to obtain a locally convergent iterative procedure. Related problems based on maximum entropy or minimum information are discussed. 相似文献
13.
The maximum entropy method for linear ill-posed problems with modeling error and noisy data is considered and the stability
and convergence results are obtained. When the maximum entropy solution satisfies the “source condition”, suitable rates of
convergence can be derived. Considering the practical applications, ana posteriori choice for the regularization parameter is presented. As a byproduct, a characterization of the maximum entropy regularized
solution is given. 相似文献
14.
We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. 相似文献
15.
A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under interval-valued intuitionistic fuzzy environment for the some situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a decision matrix provided as interval-valued intuitionistic fuzzy sets (IVIFSs), we propose two entropy measures for IVIFSs and establish an entropy weight model, which can be used to determine the criteria weights on alternatives, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the values of the weighted correlation coefficients. Finally, two applied examples demonstrate the applicability and benefit of the proposed method: it is capable for handling the multicriteria fuzzy decision-making problems with completely unknown weights for criteria. 相似文献
16.
The problem of maximizing the entropy subject to simple constraint sets is reformulated as a structured variational inequality problem by introducing dual variables. A new iterative alternating direction method is then developed that generates alternatively the dual and primal iterates. For some existing maximum entropy problems in the literature, the new dual iterate can be derived from a simple projection and then the new primal iterate can be obtained via solving approximately n separate one-dimensional strong monotone equations. Therefore, the proposed method is very easy to carry out. Preliminary numerical results show that the method is applicable. 相似文献
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In this expository article, we study optimization problems specified via linear and relative entropy inequalities. Such relative entropy programs (REPs) are convex optimization problems as the relative entropy function is jointly convex with respect to both its arguments. Prominent families of convex programs such as geometric programs (GPs), second-order cone programs, and entropy maximization problems are special cases of REPs, although REPs are more general than these classes of problems. We provide solutions based on REPs to a range of problems such as permanent maximization, robust optimization formulations of GPs, and hitting-time estimation in dynamical systems. We survey previous approaches to some of these problems and the limitations of those methods, and we highlight the more powerful generalizations afforded by REPs. We conclude with a discussion of quantum analogs of the relative entropy function, including a review of the similarities and distinctions with respect to the classical case. We also describe a stylized application of quantum relative entropy optimization that exploits the joint convexity of the quantum relative entropy function. 相似文献
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