NDLI: Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

Content Provider	Springer Nature Link
Author	Kolotilina, Lilia Yu.
Copyright Year	2006
Abstract	Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed.
Starting Page	247
Ending Page	280
Page Count	34
File Format	PDF
ISSN	10171398
Journal	Numerical Algorithms
Volume Number	42
Issue Number	3-4
e-ISSN	15729265
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2006-10-07
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Perron root nonnegative matrices spectral radius diagonal dominance singularity/nonsingularity eigenvalue inclusion sets directed graphs block-partitioned matrices Theory of Computation Algebra Mathematics Algorithms Numeric Computing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets