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1.
The notion of a low rank update arises in many important applications. This paper deals with the inverse problem of updating a rectangular matrix by additive low rank matrices so as to reposition the associated singular values. The setting is analogous to the classical pole assignment problem where eigenvalues of a square matrix are relocated. Precise and easy-to-check necessary and sufficient conditions under which the problem is solvable are completely characterized, generalizing some traditional Weyl inequalities for singular values. The constructive proof makes it possible to compute such a solution numerically. A pseudo algorithm is outlined.
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M.R. Dostani? 《Journal of Mathematical Analysis and Applications》2011,375(2):677-684
In this paper we find the first term in the asymptotics of singular values of the generalized fractional integration operator. 相似文献
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Chang Heon Kim 《The Ramanujan Journal》2009,19(2):237-246
Let p be a prime for which the congruence group Γ0(p)* is of genus zero, and j
p
* be the corresponding Hauptmodul. We investigate the twisted traces of singular values of j
p
* and construct infinite products related to them.
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-331-C00006). 相似文献
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Prabir Burman 《Journal of Mathematical Analysis and Applications》2007,327(1):251-256
From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and V? and Gorenflo [Kim Tuan V?, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order α>0 is approximately (πj)−α for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is (πj)−α[1+O(j−1)]. 相似文献
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Vladimir Nikiforov 《Linear algebra and its applications》2011,435(10):2394-2401
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. The trace norm is just one of the Ky Fan k-norms, given by the sum of the k largest singular values, which are studied more generally in the present paper. Several relations to chromatic number, spectral radius, spread, and to other fundamental parameters are outlined. Some results are extended to more general matrices. 相似文献
7.
We prove that the Gini mean values S(a,b; x,y) are Schur harmonic convex with respect to (x,y)∈(0,∞)×(0,∞) if and only if (a, b) ∈{(a, b):a≥0,a ≥ b,a+b+1≥0}∪{(a,b):b≥0,b≥a,a+b+1≥0} and Schur harmonic concave with respect to (x,y) ∈ (0,∞)×(0,∞) if and only if (a,b)∈{(a,b):a≤0,b≤0,a|b|1≤0}. 相似文献
8.
Michael Stewart 《Linear algebra and its applications》2006,419(1):53-77
This paper gives SVD perturbation bounds and expansions that are of use when an m × n, m ? n matrix A has small singular values. The first part of the paper gives subspace bounds that are closely related to those of Wedin but are stated so as to isolate the effect of any small singular values to the left singular subspace. In the second part first and second order approximations are given for perturbed singular values. The subspace bounds are used to show that all approximations retain accuracy when applied to small singular values. The paper concludes by deriving a subspace bound for multiplicative perturbations and using that bound to give a simple approximation to a singular value perturbed by a multiplicative perturbation. 相似文献
9.
The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ R × R is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : a 0, b 0, a + b 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : b 0, b a, a + b 1} ∪ {(a, b) : a 0, a b, a + b 1}. 相似文献
10.
Xingzhi Zhan 《Linear and Multilinear Algebra》2000,47(2):191-194
We pose some problems on the Hadamard product and singular values of matrices. 相似文献
11.
Xingzhi Zhan 《Linear and Multilinear Algebra》2013,61(2):191-194
We pose some problems on the Hadamard product and singular values of matrices. 相似文献
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13.
Milutin R. Dostanic 《Proceedings of the American Mathematical Society》2002,130(6):1755-1764
We prove a second order formula concerning distribution of singular values of Toeplitz matrices in some cases when conditions of the H. Widom Theorem are not satisfied.
14.
潘飚 《纯粹数学与应用数学》2003,19(2):131-136
设f(z)是复平面上的超越整函数,本文在f(z)的级满足一定限制下证明了复平面上存在一条从原点出发的射线OR,使得以OR为分角线的任意小角域内f(z)与其导函数f(z)至多只有一个IM公共值。 相似文献
15.
We study the behaviour of the smallest singular value of a rectangular random matrix, i.e., matrix whose entries are independent random variables satisfying some additional conditions. We prove a deviation inequality and show that such a matrix is a “good” isomorphism on its image. Then, we obtain asymptotically sharp estimates for volumes and other geometric parameters of random polytopes (absolutely convex hulls of rows of random matrices). All our results hold with high probability, that is, with probability exponentially (in dimension) close to 1. 相似文献
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The purpose of this paper is to provide the convergence theory for the iterative approach given by M.T. Chu [Numerical methods for inverse singular value problems, SIAM J. Numer. Anal. 29 (1992), pp. 885–903] in the context of solving inverse singular value problems. We provide a detailed convergence analysis and show that the ultimate rate of convergence is quadratic in the root sense. Numerical results which confirm our theory are presented. It is still an open issue to prove that the method is Q-quadratic convergent as claimed by M.T. Chu. 相似文献
19.
M. Loayza 《Journal of Differential Equations》2006,229(2):509-528
We study the existence, uniqueness and regularity of positive solutions of the parabolic equation ut−Δu=a(x)uq+b(x)up in a bounded domain and with Dirichlet's condition on the boundary. We consider here a∈Lα(Ω), b∈Lβ(Ω) and 0<q?1<p. The initial data u(0)=u0 is considered in the space Lr(Ω), r?1. In the main result (0<q<1), we assume a,b?0 a.e. in Ω and we assume that u0?γdΩ for some γ>0. We find a unique solution in the space . 相似文献
20.
We give refined statements and modern proofs of Rosenlicht’s results about the canonical model C′ of an arbitrary complete integral curve C. Notably, we prove that C and C′ are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equal to the blowup of C with respect to the canonical sheaf
ω. We also prove some new results: we determine just when C′ is rational normal, arithmetically normal, projectively normal, and linearly normal.
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