共查询到19条相似文献,搜索用时 140 毫秒
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对多变量线性系统,本文给出了求其逆向系统的一种新方法,这种方法将逆向系统计算中高阶矩阵的求逆转化为通过初等变换求低阶矩阵的规范型,比以往的方法更加简单有效且易于编程计算。本文结合系统的可观测空间与不可观测空间的情况,给出了一种特定的等价变换,得到了比通常更低阶的逆向系统。 相似文献
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利用矩阵分块逐次降阶的方法和快速富里叶变换(FFT),给出了mn阶(R,r)-循环分块矩阵求逆与相乘的一种快速算法,证明了其计算复杂性为O(mnlog2mn). 相似文献
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降阶方法是处理矩阵问题的最核心的思想方法之一.从分块矩阵■出发,利用降阶的思想,讨论了该矩阵的逆与秩的计算,并给出该降阶公式的各种变形以及在解题中的应用. 相似文献
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分块带状矩阵的逆 总被引:1,自引:0,他引:1
1引言如果分块矩阵A=(A_(ij))_(n×n)满足A_(ij)=O(j-i>p且i-j>q),其中A_(ij)为m阶矩阵,则称A为(p,q)-分块带状矩阵.分块带状矩阵在一些实际问题中经常出现,例如在量子场论中用途很广的非线性Schr(?)dinger方程的差分离散问题,解热传导问题等,都会遇到分块带状矩阵.常见的分块三对角矩阵,分块五对角矩阵都是特殊的分块带状矩阵.采用通常的方法求解分块带状矩阵的逆矩阵时,需要进行O(n~3)次m阶矩阵的运算.本文首先将分块带状矩阵扩充成可逆的分块上(下)三角矩阵,利用其逆矩阵导出了分块带状矩阵的逆矩阵表达式;进而利用所得到的公式分别推导了分块三对角矩阵及分块五对角矩阵的逆矩阵的快速算法,所需运算量为O(n~2)次m阶矩阵的运算.本文的结果扩充了文[1]等关于分块三对角阵求逆的相关结果. 相似文献
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R. Srinivasan Puri Denise Morrey Andrew J. Bell John F. Durodola Evgenii B. Rudnyi Jan G Korvink 《Applied Mathematical Modelling》2009
A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS. 相似文献
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The inversion of polynomial and rational matrices is considered. For regular matrices, three algorithms for computing the
inverse matrix in a factored form are proposed. For singular matrices, algorithms of constructing pseudoinverse matrices are
considered. The algorithms of inversion of rational matrices are based on the minimal factorization which reduces the problem
to the inversion of polynomial matrices. A class of special polynomial matrices is regarded whose inverse matrices are also
polynomial matrices. Inversion algorithms are applied to the solution of systems with polynomial and rational matrices. Bibliography:
3 titles.
Translated by V. N. Kublanovskaya.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 97–109. 相似文献
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The Moor-Penrose generalized inverses (M-P inverses for short) of matrices over a finite field Fq2, which is a generalization of the Moor-Penrose generalized inverses over the complex field, are studied in the present paper. Some necessary and sufficient conditions for an m×n matrix A over Fq2 having an M-P inverse are obtained, which make clear the set of m×n matrices over Fq2 having M-P inverses and reduce the problem of constructing and enumerating the M-P invertible matrices to that of constructing and enumerating the non-isotropic subspaces with respect to the unitary group. Based on this reduction, both the construction problem and the enumeration problem are solved by borrowing the results in geometry of unitary groups over finite fields. 相似文献
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C. Koukouvinos 《Discrete Mathematics》2008,308(13):2723-2731
Skew-Hadamard matrices are of special interest due to their use, among others, in constructing orthogonal designs. In this paper, we give a survey on the existence and equivalence of skew-Hadamard matrices. In addition, we present some new skew-Hadamard matrices of order 52 and improve the known lower bound on the number of the skew-Hadamard matrices of this order. 相似文献
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In this paper, we consider the conjugate-Toeplitz (CT) and conjugate-Hankel (CH) matrices. It is proved that the inverse of these special matrices can be expressed as the sum of products of lower and upper triangular matrices. Firstly, we get access to the explicit inverse of conjugate-Toeplitz matrix. Secondly, the decomposition of the inverse is obtained. Similarly, the formulae and the decomposition on inverse of conjugate-Hankel are provided. Thirdly, the stability of the inverse formulae of CT and CH matrices are discussed. Finally, examples are provided to verify the feasibility of the algorithms provided in this paper. 相似文献
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In this paper, a symmetric nonnegative matrix with zero diagonal and given spectrum, where exactly one of the eigenvalues is positive, is constructed. This solves the symmetric nonnegative eigenvalue problem (SNIEP) for such a spectrum. The construction is based on the idea from the paper Hayden, Reams, Wells, “Methods for constructing distance matrices and the inverse eigenvalue problem”. Some results of this paper are enhanced. The construction is applied for the solution of the inverse eigenvalue problem for Euclidean distance matrices, under some assumptions on the eigenvalues. 相似文献
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J.R. Wall 《Linear algebra and its applications》1975,10(2):147-154
This paper describes all stochastic matrices which have a stochastic semi-inverse and gives a method of constructing all such inverses. Then all stochastic matrices which have a stochastic Moore-Penrose inverse are described. 相似文献
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Shumin Li 《Applicable analysis》2013,92(11):2287-2307
In this paper, we consider Carleman-type estimate and consider an inverse problem for second order hyperbolic systems in an anisotropic case. In the previous Part I paper, we established a Carleman-type estimate for hyperbolic systems in which the coefficient matrices satisfy suitable conditions. We apply a Carleman estimate in the previous Part I paper to an inverse source problem for second-order hyperbolic systems in an anisotropic case and prove an estimate of the Hölder type. 相似文献
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基于Schmidt正交化过程获得了一种计算逆矩阵的新方法.对于可逆矩阵A,有Q=MA,其中Q是酉矩阵,M是下三角矩阵.本文直接从Schmidt规范正交化出发,获得下三角矩阵M的计算公式,从而求得逆矩阵A-1=QHM=AHMTM. 相似文献