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1.
矩阵奇异值的下界估计 总被引:2,自引:0,他引:2
本文中总记mxn复(实)矩阵空间以C"""(R"""),q二min{。,n).设A一(a;。)e*-"-,A的q个奇异值按递减次序排列为。1川三。2(AZ...Z内科三0.对A的奇异值,特别是最小奇异值的下界估计,是矩阵分析的重要课题,在目前已有重要估计【回叫,C.R.Johnson给出的下述最小奇异值下界估计是最好的结果11]:矩阵Cassini型谱包含域得到了矩阵奇异值的一个下界估计式.进而给出了达到下界估计式时的矩阵表征,所得结果改进了山一[4]之相应结果.我们首先讨论方阵的情况.引理1.设A二(。ti)EC""",人()={Al(A),...,A… 相似文献
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《数学的实践与认识》2017,(18)
通过对母矩阵进行奇异值分解的方法得到广义行(列)酉对称矩阵的奇异值分解进一步得到其Moore-penrose逆;用谱分解方法得到母矩阵的Moore-penrose逆,进一步得到广义行(列)酉对称矩阵的Moore-penrose逆. 相似文献
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讨论了矩阵奇异值的问题,利用奇异值分解定理给出了奇异值的极值性质,并用其证明了矩阵论中关于奇异值的一些经典结论. 相似文献
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O-对称矩阵的奇异值分解及其算法 总被引:3,自引:0,他引:3
本文研究了具有轴对称结构矩阵的奇异值分解,找出了这类矩阵奇异值分解与其子阵奇异值分解之间的定量关系.利用这些定量关系给出这类矩阵奇异值分解和Moore-Penrose逆的算法,据此可极大地节省求该类矩阵奇异值分解和Moore-Penrose逆时的计算量和存储量. 相似文献
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刘晓冀 《数学的实践与认识》2008,38(2):108-114
研究矩阵的奇异值偏序,给出了矩阵的奇异值偏序的等价刻画和性质,指出了相关文献关于矩阵*序刻画不真,利用强同时奇异值分解给出了矩阵*-序的刻画. 相似文献
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M. E. Fernandes Miranda 《Linear and Multilinear Algebra》1981,10(2):155-161
In this paper we prove several inequalities involving the characteristic values, the singular values, the real singular values and the imaginary singular values of a complex matrix. 相似文献
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The iterative computation of singular points in parametrized nonlinear BVPs by so-called extended systems requires good starting values for the singular point itself and the corresponding eigenfunction. Using path-following techniques such starting values for the singular points should be generated automatically. However, path-following does not provide approximations for the eigenfunction if the singularity is a bifurcation point. We propose a new modification of this standard technique delivering such starting values. It is based on an extended system by which singular as well as nonsingular points can be determined. 相似文献
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Nadaniela Egidi 《Journal of Mathematical Analysis and Applications》2011,377(2):670-682
We consider the integral operator defined on a circular disk, and with kernel the Green function of the Helmholtz operator. We present an analytic framework for the explicit computation of the singular system of this kernel. In particular, the main formulas of this framework are given by a characteristic equation for the singular values and explicit expressions for the corresponding singular functions. We provide also a property of the singular values, that gives an important information for the numerical evaluation of the singular system. Finally, we present a simple numerical experiment, where the singular system computed by a simple implementation of these analytic formulas is compared with the singular system obtained by a discretization of the Green function of the Helmholtz operator. 相似文献
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Summary.
In this paper we propose an algorithm based on Laguerre's iteration,
rank two divide-and-conquer technique and a hybrid strategy
for computing singular values of bidiagonal matrices.
The algorithm is fully parallel in nature and evaluates singular
values to tiny relative error if necessary. It is competitive with QR
algorithm in serial mode in speed and advantageous in computing
partial singular values. Error analysis and numerical results are
presented.
Received
March 15, 1993 / Revised version received June 7, 1994 相似文献
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殷庆祥 《高等学校计算数学学报》2003,25(4):351-361
The eigenvalues and singular values are two of the most distinguished characteristics in a square matrix. Weyl has proved the majorization between them. Horn has proved its inverse, i.e. there exists a matrix with prescribed eigenvalues and singular values. This paper presents a direct transform method which shows the matrix can be upper triangular with its diagonal elements in any order. There exists a real-valued matrix with prescribed complex-conjugate eigenvalues and singular values. Construction of matrices with mixed data is also considered. 相似文献
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A highly accurate computation of the singular values of a matrix is a topic of current interest in the literature. In this paper we develop general bounds on relative perturbation of singular values. These bounds permit slight improvements in a unified derivation of some previous inequalities. The main result is a better criterion to neglect off-diagonal elements in the bidiagonal singular values decomposition.The present paper has been developed under the M. U. R. S. T. 40% National Program and the Interuniversity Center of Numerical Analysis and Computational Mathematics. 相似文献
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Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann‐Hilbert Problem Approach 下载免费PDF全文
We study the asymptotics of singular values and singular functions of a finite Hilbert transform (FHT), which is defined on several intervals. Transforms of this kind arise in the study of the interior problem of tomography. We suggest a novel approach based on the technique of the matrix Riemann‐Hilbert problem (RHP) and the steepest‐descent method of Deift‐Zhou. We obtain a family of matrix RHPs depending on the spectral parameter λ and show that the singular values of the FHT coincide with the values of λ for which the RHP is not solvable. Expressing the leading‐order solution as λ → 0 of the RHP in terms of the Riemann Theta functions, we prove that the asymptotics of the singular values can be obtained by studying the intersections of the locus of zeroes of a certain Theta function with a straight line. This line can be calculated explicitly, and it depends on the geometry of the intervals that define the FHT. The leading‐order asymptotics of the singular functions and singular values are explicitly expressed in terms of the Riemann Theta functions and of the period matrix of the corresponding normalized differentials, respectively. We also obtain the error estimates for our asymptotic results. © 2016 Wiley Periodicals, Inc. 相似文献