Block diagonal dominance of matrices revisited: bounds for the norms of inverses and eigenvalue inclusion sets

We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this gen...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: Echeverría, Carlos, Liesen, Jörg, Nabben, Reinhard
Format: Article
Language:English
Subjects:
Eigenvalues
Norms
Online Access:Get full text
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Summary:We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this generalization, which was recently presented in [3], we also derive a variant of the Gershgorin Circle Theorem for general block matrices which can provide tighter spectral inclusion regions than those obtained by Feingold and Varga.
ISSN:2331-8422