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

2017/12/15 by Echeverría, Carlos, Liesen, Jörg, Nabben, Reinhard · 2 citations
#15A45 #65F15 #FOS: Mathematics #Numerical Analysis (math.NA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1712.05662

Abstract

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.

Cited by

• Hidden decay in the inverses of acyclic matrices
• Quasiseparable LU decay bounds for inverses of banded matrices

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