Block Diagonal Dominance of Matrices Revisited: Bounds for the Norms of Inverses and Eigenvalue Inclusion Sets
arXiv (Cornell University)(2017)
摘要
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.
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Matrix Computations
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