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求解线性矩问题的一个修正方法 总被引:5,自引:0,他引:5
1.引言许多问题都可化为线性矩问题的求解,最典型的例子就是求解第一类线性积分方程的配置法.第一类算子方程在不同国数空间的离散化得到不同形式的线性矩问题.1968年,地质学家GBackusandFGilbert给出了一种求解线性矩问题的方法,用来求解地球物理反问题,后来称之为B-G方法,山从理论上严格论证了其收敛性.问给出了一种求解线形矩问题的光顺方法,门讨论了再生核空间的rG方法,并将其用于信号处理.以上方法的核心思想是在某类函数空间寻求对利一函数的逼近,从而得到线性矩问题的近似解.本交给出了一种求解线性矩问题的修正方… 相似文献
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Demyanov和Rubinov在[1]中给出了一个次线性逼近定理.本文对该定理的证明进行了修正. 相似文献
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线性流形上的矩阵最佳逼近 总被引:7,自引:1,他引:7
戴华 《高校应用数学学报(A辑)》1994,(3):312-320
令S={A∈Rn×m|f1(A)=‖AX1-Z1‖2+‖YT1A-WT1‖2=min},其中X1∈Rm×k1,Z1∈Rn×k1,Y1∈Rn×11和W1∈Rm×11均为给定的矩阵,‖·‖是Frobenius范数。本文考虑如下问题:问题Ⅰ给定X2∈Rm×k2,Z2∈Rn×k2,Y2∈Rn×l2,W2∈Rm×l2,求A∈S,使得f2(A)=‖AX2-Z2‖2+‖YT2A-WT2‖2=min.问题Ⅱ给定A∈Rn×m,求A∈SA,使得‖A-A‖=infA∈SA‖A-A‖,其中SA是问题I的解集合。本文给出问题I解集合SA的通式和问题Ⅱ的解A的表达式,提出了求解问题Ⅰ与Ⅱ的数值方法。许多文献的结果都是本文结果的特例。 相似文献
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本文给出并证明了拓扑σ(L^∞,L^1)下线性算子逼近L^∞函数的Korovkin定理。 相似文献
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线性流形上的两类矩阵最佳逼近问题 总被引:6,自引:0,他引:6
1.引言设R”””表示所有实mxn阶矩阵的全体,OR”””表示所有n阶正交阵的全体,对于A=(ail)eR”””,B=(b;j)eRP”’,用A@BeR’”“”’表示矩阵A与B的Kronecker积,用A二(all,ala,…,al。,aal,…aa。,…;a_l,…,a_*“表m矩阵A拉直算子,l]·IF表示矩阵的Frobenius范数,11·11。表示向量的2一范数.设S={X,X6R”””f(X)二llAIXBI—Dlll》+IIAZXBZ—D。股一Zill}其中AlER”X”,BIERPXq,DIER”XqAZERtX”BZERPXIDZERtXI考虑下列两类问题:问题I.给定CIERll“”.FIE… 相似文献
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随着分段线性函数的广泛应用,本文尝试研究浅层和深层的分段线性神经网络的逼近理论.作者将应用于三层感知机模型的万能逼近定理拓展到分段线性神经网络中,并给出与隐藏神经元个数相关的逼近误差估计.利用分段线性函数构造锯齿函数的显式方法,证明解析函数可以通过分段线性神经网络的深度堆叠以指数速率逼近,并辅以相应的数值实验. 相似文献
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线性流形上中心对称矩阵的最佳逼近 总被引:9,自引:1,他引:9
1 引 言令Rn×m表示所有n×m阶实矩阵集合;ORn×n表示所有n×n阶正交矩阵之集;A+表示矩阵A的Moore-Penrose广义逆;Iκ表示κ阶单位阵;||·||表示矩阵的Frobenius范数;rank(A)表示矩阵A的秩.设ei为n阶单位矩阵In的第i列(i=1,2,…,n),记Sn=(en,en-1,…,e1),易知 相似文献
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Charles B. Dunham 《Journal of Computational and Applied Mathematics》1984,11(2):139-143
The linear inequality method is an algorithm for discrete Chebyshev approximation by generalized rationals. Stability of the method with respect to uniform convergence is studied. Analytically, the method appears superior to all others in reliability. 相似文献
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《Optimization》2012,61(6):839-860
This paper introduces an efficient approach to the solution of the linear mini-max approximation problem. The classical nonlinear minimax problem is cast into a linear formulation. The proposed optimization procedure consists of specifying first a feasible point belonging to the feasible boundary surface. Next, feasible directions of decreasing values of the objective function are determined. The algorithm proceeds iteratively and terminates when the absolute minimum value of the objective function is reached. The initial point May be selected arbitrarily or it May be optimally determined through a linear method to speed up algorithmic convergence. The algorithm was applied to a number of approximation problems and results were compared to those derived using the revised simplex method. The new algorithm is shown to speed up the problem solution by at least on order of magnitude. 相似文献
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Chia-Hui Huang 《Applied mathematics and computation》2009,215(4):1496-1506
Among the numerous applications of piecewise linearization methods include data fitting, network analysis, logistics, and statistics. In the early 1950s, a concave function was found to be able to be linearized by introducing 0-1 variables. Most textbooks in Operations Research offer such methods for expressing linear approximations. Various methods of linearization have also been developed in recent literature. Nevertheless, the transformed linear scheme has a severe shortcoming: most standard procedures for linearizing typically involve a large increase in the number of binary variables. Consequently, the gains to be derived from dealing with linear functions are quite likely to be nullified by the increase in the size of the problem.Conventional methods for linearizing a concave function with m break points require m-1 binary variables. However, when m becomes large, the computation will be very time-consuming and may cause a heavy computational burden.This study proposes an effective approach in which only ⌈log2(m-1)⌉ binary variables are used. The proposed method has the following features: (i) it offers more convenient and efficient means of expressing a piecewise linear function; (ii) fewer 0-1 variables are used; (iii) the computational results show that the proposed method is much more efficient and faster than the conventional one, especially when the number of break points becomes large. 相似文献
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设施布局问题的研究始于20世纪60年代,主要研究选择修建设施的位置和数量,以及与需要得到服务的城市之间的分配关系,使得设施的修建费用和设施与城市之间的连接费用之和达到最小.现实生活中, 受自然灾害、工人罢工、恐怖袭击等因素的影响,修建的设施可能会出现故障, 故连接到它的城市无法得到供应,这就直接影响到了整个系统的可靠性.针对如何以相对较小的代价换取设施布局可靠性的提升,研究人员提出了可靠性设施布局问题.参考经典设施布局问题的贪婪算法、原始对偶算法和容错性问题中分阶段分层次处理的思想,设计了可靠性设施布局问题的一个组合算法.该算法不仅在理论上具有很好的常数近似度,而且还具有运算复杂性低的优点.这对于之前的可靠性设施布局问题只有数值实验算法, 是一个很大的进步. 相似文献
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In this paper, an iterative algorithm based on the Landwebermethod in combination with the boundary element method is developedfor solving the Cauchy problem in isotropic linear elasticity.An efficient regularizing stopping criterion is also employed.The numerical results obtained confirm that the iterative methodproduces a convergent and stable numerical solution with respectto increasing the number of boundary elements and decreasingthe amount of noise added into the input data, respectively. 相似文献
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By the method of geometry of Banach spaces, we have proven that a bounded linear operator in Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rank bounded homogeneous operators, which reveals the essence of the counter example given by Enflo. 相似文献
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This paper concerns with the statistical methods for solving general linear systems. After a brief review of Bayesian perspective for inverse problems,a new and efficient iterative method for general linear systems from a Bayesian perspective is proposed.The convergence of this iterative method is proved,and the corresponding error analysis is studied.Finally, numerical experiments are given to support the efficiency of this iterative method,and some conclusions are obtained. 相似文献
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An interior point algorithm for semi-infinite linear programming 总被引:3,自引:0,他引:3
We consider the generalization of a variant of Karmarkar's algorithm to semi-infinite programming. The extension of interior point methods to infinite-dimensional linear programming is discussed and an algorithm is derived. An implementation of the algorithm for a class of semi-infinite linear programs is described and the results of a number of test problems are given. We pay particular attention to the problem of Chebyshev approximation. Some further results are given for an implementation of the algorithm applied to a discretization of the semi-infinite linear program, and a convergence proof is given in this case. 相似文献
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《Optimization》2012,61(6):905-911
In this paper so-called ε-approximations for the efficiency set of vector minimization problems are defined. A general generating algorithm for such E-approximations is given which will be modified for linear continuous problems by means of the Dual Simplex Method. 相似文献