کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602620 1631171 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Inclusion sets for singular values
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Inclusion sets for singular values
چکیده انگلیسی

In this paper, the following inclusion sets are under certain conditions presented for singular values of a matrix A=[aij]∈Cn×nA=[aij]∈Cn×n:D(A)≔⋃γ∈C(A)0:∏i∈γ∣z-ai∣⩽∏i∈γ(ρ(B)-bii)}andKP(A)≔⋃i=1n⋃j∈Pi(A){z⩾0:∣z-ai∣∣z-aj∣⩽(ρ(B)-bii)(ρ(B)-bjj)},where ai=∣aii∣ai=∣aii∣ and Pi(A)≔{j∣aij≠0oraji≠0,j≠i} for any i∈{1,2,⋯,n}i∈{1,2,⋯,n}, ρ(B  ) and C(A)C(A) denote the Perron root of the nonnegative matrix B=[bij]B=[bij] satisfying ∣aij∣,∣aji∣⩽bij∣aij∣,∣aji∣⩽bij for all i,j∈{1,2,⋯,n}i,j∈{1,2,⋯,n} with i≠ji≠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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issues 8–9, 15 April 2008, Pages 2220–2235
نویسندگان
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