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Inclusion sets for singular values

✍ Scribed by Hou-Biao Li; Ting-Zhu Huang; Hong Li

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
320 KB
Volume
428
Category
Article
ISSN
0024-3795

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✦ Synopsis

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

where a i = |a ii | and P i (A) := {j |a ij / = 0 or a ji / = 0, j / = i} for any i ∈ {1, 2, . . . , n}, ρ(B) and C(A) denote the Perron root of the nonnegative matrix B =[b ij ] satisfying |a ij |, |a ji | b ij for all i, j ∈{1, 2, . . . , n} with i / = j and the set of all nontrivial circuits γ in (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.

πŸ“œ SIMILAR VOLUMES

Optimal Gerschgorin-type inclusion inter
Optimal Gerschgorin-type inclusion intervals of singular values
✍ Hou-Biao Li; Ting-Zhu Huang; Hong Li; Shu-Qian Shen πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 142 KB

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Initial value problems for singular and
Initial value problems for singular and nonsmooth second order differential inclusions
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## Abstract We study the existence of __W__^2,1^ solutions for singular and nonsmooth initial value problems of the type equation image where__T__ > 0 is a priori fixed, __x__~0~, __x__~1~ ∈ ℝ, and __F__: [0, __T__ ] Γ— ℝ β†’ 𝒫(ℝ) \ {βˆ…οΈ} is a multivalued mapping. (Β© 2007 WILEY‐VCH Verlag GmbH & Co.