Inclusion sets for singular values

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• 作者：Hou-Biao Li ; Ting-Zhu Huang ; Hong Li
• 关键词：Singular value ; Nonnegative matrix ; Condition number
• 刊名：Linear Algebra and its Applications
• 出版年：2008
• 出版时间：15 April 2008
• 年：2008
• 卷：428
• 期：8-9
• 页码：2220-2235
• 全文大小：320 K

文摘

In this paper, the following inclusion sets are under certain conditions presented for singular values of a matrix :

and

where a_i=a_ii and for any i{1,2,,n}, ρ(B) and denote the Perron root of the nonnegative matrix B=[b_ij] satisfying a_ij,a_jib_ij for all i,j{1,2,,n} with i≠j and the set of all nontrivial circuits γ in Γ(A)—the associated directed digraph of A, respectively. Subsequently, relations between these two results are investigated. Theoretic analysis and numerical examples show that these estimates are more precise than recent corresponding results in some cases.