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51.
We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph. 相似文献
52.
An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szegő is under consideration. An analog of the Fejér—Riesz representation of nonnegative
general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials
for the problem of Rogosinski and Szegő are obtained explicitly. Associated cosine polynomials k
n
(θ) are constructed in such a way that { k
n
(θ) } are summability kernels. Thus, the L
p
, pointwise and almost everywhere convergence of the corresponding convolutions, is established.
April 26, 2000. Date revised: December 28, 2000. Date accepted: February 8, 2001. 相似文献
53.
Anthony G. Cronin 《Linear and Multilinear Algebra》2018,66(3):435-446
We present and compare three constructive methods for realizing nonreal spectra with three nonzero elements in the nonnegative inverse eigenvalue problem. We also provide some necessary conditions for realizability and numerical examples. In particular, we utilize the companion matrix. 相似文献
55.
56.
Thomas J. Laffey 《Linear algebra and its applications》2008,428(1):230-238
Let A be an n×n nonnegative matrix with the spectrum (λ1,λ2,…,λn) and let A1 be an m×m principal submatrix of A with the spectrum (μ1,μ2,…,μm). In this paper we present some cases where the realizability of (μ1,μ2,…,μm,ν1,ν2,…,νs) implies the realizability of (λ1,λ2,…,λn,ν1,ν2,…,νs) and consider the question whether this holds in general. In particular, we show that the list
(λ1,λ2,…,λn,-μ1,-μ2,…,-μm) 相似文献
57.
Thomas J. Laffey 《Linear algebra and its applications》2007,421(1):97-109
Let σ = (λ1, … , λn) be the spectrum of a nonnegative symmetric matrix A with the Perron eigenvalue λ1, a diagonal entry c and let τ = (μ1, … , μm) be the spectrum of a nonnegative symmetric matrix B with the Perron eigenvalue μ1. We show how to construct a nonnegative symmetric matrix C with the spectrum
(λ1+max{0,μ1-c},λ2,…,λn,μ2,…,μm). 相似文献
58.
In this paper, we show that the semilinear elliptic systems of the form
(0.1) 相似文献
59.
A modified algorithm for the Perron root of a nonnegative matrix 总被引:1,自引:0,他引:1
Chengming Wen Ting-Zhu Huang 《Applied mathematics and computation》2011,217(9):4453-4458
An algorithm of diagonal transformation for the Perron root of nonnegative matrices is proposed by Duan and Zhang [F. Duan, K. Zhang, An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices, Appl. Math. Comput. 175 (2006) 762-772]. This method can be used for all nonnegative irreducible matrices. In this paper, an improved algorithm which is based on this method is proposed. The new algorithm inherits all the above-mentioned advantages of the original algorithm and has higher efficiency. It is testified by numerical testing that the efficiency of the new algorithm is improved greatly. 相似文献
60.
The main aim of this article is to deal with the almost-sure stability of stochastic differential delay equations. Our improved theorems give better results while conditions imposed on the Lyapunov function are much weaker, thus, it is easier to find a right Lyapunov function in application. 相似文献