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基于部分基变量提出了LP问题的矩阵算法. 该算法以最优基矩阵的一个充分必要条件为基础,首先将一个初始矩阵转化为右端项和检验数均满足要求的矩阵,再转为检验数满足要求的基矩阵,最后转化为最优基矩阵.该算法具有使用范围广、计算规模小、计算过程简化、计算机易于实现的优势.矩阵算法的核心运算是求逆矩阵的运算,提出了矩阵算法的求逆问题,讨论并给出了求逆快速算法,该算法充分利用了矩阵算法迭代过程中提供的原来的逆矩阵的信息经过简单的变换得到新的逆矩阵,该算法比直接求逆法计算效率更高. 相似文献
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《应用数学与计算数学学报》2016,(2)
伪谱是解释非正规矩阵或算子行为的一个有用工具.矩阵伪谱计算的一个常用方法是grid-SVD算法,实现这个算法需要在每一个网格点处作奇异值分解(SVD);另外一个计算方法是基于Schur分解的逆Lanczos算法.由于上述方法的计算量比较大,通常只适用于中小型矩阵.近些年,有些学者探讨了大规模矩阵伪谱计算的Krylov子空间投影方法.在探讨了Householder Arnoldi(HA)算法块情形的计算行为和实用性能的基础上,提出了计算大规模矩阵伪谱的增广块HA(ABHA)算法,并对一些典型测试矩阵进行了一系列的数值试验.数值结果表明,增广块HA(ABHA)算法比HA算法,块隐式重启Arnoldi(BLIRA)算法和逆Lanczos算法的计算效率更高,更具优越性. 相似文献
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给出了判定非奇异M-矩阵的一个直接算法.数值例子表明应用该算法可有效地判定一个给定矩阵是否为非奇异M-矩阵. 相似文献
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矩阵的Jordan标准型的变换矩阵的计算方法 总被引:1,自引:0,他引:1
蒋尔雄 《高等学校计算数学学报》1979,(1)
本文给出一种计算任意复方阵的Jordan标准形的变换矩阵的算法,并证明按照给出的算法计算结果得到的一个矩阵确是所要求的Jordan标准形的变换矩阵。 相似文献
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本文提出一种算法 ,利用该算法可在给定的一致性指标下求得一个新的判定矩阵 .新矩阵与原矩阵具有相同的主特征向量 ,而且有助于判断原矩阵的可靠性 相似文献
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曹志浩 《高等学校计算数学学报》1988,(4)
对n×n对称奇异矩阵束A-λB应用对称收缩方法导出了一个可以成对地抽出Kronecker行指标和Kronecker列指标以及同时抽出无穷初等因子的算法。由于充分利用了矩阵束A-λB的对称性,因而我们的算法比其它已有的算法更有效。经算法收缩后的矩阵束仍是对称的,但只包含有限初等除式(因而是一个特殊的对称正则矩阵束)。原矩阵束所对应的对称广义特征值问题经收缩后约化为一个只含有限特征值的对称广义特征值问题,因而易于求解。 相似文献
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求解特征值反问题的一种迭代法 总被引:1,自引:0,他引:1
关于特征值反问题的算法,已讨论许多,见[1]—[5].到目前为止,主要的算法是用Newton法解相应的非线性方程组.然而,代数特征值反问题是一类矩阵计算问题,因此,有可能利用矩阵的性质构造简单的算法,而不仅仅是把它作为一个通常的非线性问题加以处理.基于这种思想.本文给出一个利用矩阵性质的线性收敛迭代法. 相似文献
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《数学的实践与认识》2019,(7)
二元矩阵M_q(n,k,d)是一个非适应性分组测试(NGT)算法的数学模型,它是一个d-析取矩阵.在矩阵M_q(n,k,d)的基础上研究它的子矩阵M_q(n.k,d,z)的检纠错性质. 相似文献
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主要研究对称正定矩阵群上的内蕴最速下降算法的收敛性问题.首先针对一个可转化为对称正定矩阵群上无约束优化问题的半监督度量学习模型,提出对称正定矩阵群上一种自适应变步长的内蕴最速下降算法.然后利用李群上的光滑函数在任意一点处带积分余项的泰勒展开式,证明所提算法在对称正定矩阵群上是线性收敛的.最后通过在分类问题中的数值实验说明算法的有效性. 相似文献
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In this paper, we specialize Gill et al.'s projected Newton barrier method to solve a large-scale linear program of dynamic (i.e. multistage) Leontief-type constraints. We propose an efficient and stable method for solving the least-squares subproblems, the crucial part of the barrier method. The key step is to exploit a special structure of the constraint matrix and reduce the matrix of the normal equation for the least-squares problem to a banded matrix. By comparing the average-case operations count of this specialized barrier method with that of the sparse simplex method, we show that this method performs at least O(T) faster than the simplex method for such stype of linear programs, where T is the number of time periods (i.e. stages). 相似文献
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1.引言本文考虑如下边界约束的二次规划问题:其中QE*"""是对称的,C,人。E*"是给定的常数向量,且Z<。这类问题经常出现在偏微分方程,离散化的连续时间最优控制问题、线性约束的最小二乘问题、工程设计、或作为非线性规划方法中的序列子问题.因此具有特殊的重要性.本文提出求解问题(1.1)的分解方法.它类似求解线性代数方程组的选代法,它是对Q进行正则分裂【对即把Q分裂为两个矩阵之和,Q=N十片而这两个矩阵之差(N一则是对称正定的.在每次迭代中用一个易于求解的矩阵N替代Q进行计算一新的二次规划问题.在适… 相似文献
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模糊判断矩阵一致性逼近及排序方法 总被引:23,自引:1,他引:22
根据一致性模糊判断矩阵定义,提出了一种求取一致性判断矩阵及方案排序的新方法,该方法是通过建立一个线性目标规划模型来得到排序向量,并相应地得到逼近于决策偏好的一致性判断矩阵,最后给出了一个算例。 相似文献
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基于线性规划核心矩阵的单纯形算法 总被引:3,自引:0,他引:3
本文讨论了线性规划中的核心矩阵及其特性,探讨了利用核心矩阵实现单纯形算法的可能性,并进一步提出了一个基于核心矩阵的两阶段原始一对偶单纯形方法,该方法通过原始和对偶两个阶段的迭代,可以在有限次迭代中收敛到原问题的最优解或证明问题无解或无界.在试验的22个问题中,该算法的计算效率总体优于基于传统单纯形方法的MINOS软件. 相似文献
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The Roppenecker [11] parameterization of multi-input eigenvalue assignment, which allows for common open- and closed-loop eigenvalues, provides a platform for the investigation of several issues of current interest in robust control. Based on this parameterization, a numerical optimization method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations such that these eigenvalues have low sensitivity to variations in the open-loop state space model was presented in Owens and O'Reilly [8]. In the present paper, two closely related numerical optimization methods are presented. The methods utilize standard (NAG library) unconstrained optimization routines. The first is for designing a minimum gain state feedback matrix which assigns the closed-loop eigenvalues to desired locations, where the measure of gain taken is the Frobenius norm. The second is for designing a state feedback matrix which results in the closed-loop system state matrix having minimum condition number. These algorithms have been shown to give results which are comparable to other available algorithms of far greater conceptual complexity. 相似文献
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J. B. Lasserre 《Journal of Optimization Theory and Applications》1981,34(2):197-205
In this paper, we present a property of certain linear multistage problems. To solve them, a method which takes this property into account is presented. It requires the resolution of 2N–1 subproblems, if there areN stages in the original problem. A sufficient condition is given on the matrix of the constraints for the property to be true. When only a submatrix has this property, we propose to use the Dantzig-Wolfe decomposition principle. We then can solve the subproblem with the proposed method. Applications to linear and nonlinear programming are presented.This work was done while the author was Visiting Scholar at the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California. 相似文献
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We propose an interior point method for large-scale convex quadratic programming where no assumptions are made about the sparsity structure of the quadratic coefficient matrixQ. The interior point method we describe is a doubly iterative algorithm that invokes aconjugate projected gradient procedure to obtain the search direction. The effect is thatQ appears in a conjugate direction routine rather than in a matrix factorization. By doing this, the matrices to be factored have the same nonzero structure as those in linear programming. Further, one variant of this method istheoretically convergent with onlyone matrix factorization throughout the procedure. 相似文献
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J. T. Betts 《Journal of Optimization Theory and Applications》1976,18(4):469-483
An algorithm for solving the general nonlinear least-square problem is developed. An estimate for the Hessian matrix is constructed as the sum of two matrices. The first matrix is the usual first-order estimate used by the Gauss method, while the second matrix is generated recursively using a rank-one formula. Test results indicate that the method is superior to the standard Gauss method and compares favorably with other methods, especially for problems with nonzero residuals at the solution.This work was supported by the US Air Force under Contract No. F04701-73-C-0074.The author expresses his appreciation to Dr. H. E. Pickett and Dr. J. L. Searcy for their continuing support in the theoretical and practical development of the algorithm. The recursive method for generating the estimate of the Hessian matrix was developed jointly with Drs. Pickett and Searcy and is included here with their permission. The author would also like to acknowledge the contribution made by the stimulating environment of an optimal control seminar held at The Aerospace Corporation since 1970. Principle members of the seminar have been H. E. Pickett, J. L. Searcy, R. W. Reid, and the author. 相似文献