An upper bound for \(\| A^{-1}\|_{\infty}\) of strictly diagonally dominant \(M\)-matrices

DOI10.1016/j.laa.2007.06.001zbMath1126.15022OpenAlexW2072451235MaRDI QIDQ996319

Ting-Zhu Huang, Guang-Hui Cheng

Publication date: 14 September 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.06.001

zbMATH Keywords

normspectral radius\(M\)-matrixnonnegative matrixinverse \(M\)-matrixdiagonal dominancePerron eigenvalue

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (10)

New upper bounds for \(\|A^{-1}\|_{\infty}\) of strictly diagonally dominant \(M\)-matrices ⋮ A fast and stable test to check if a weakly diagonally dominant matrix is a nonsingular M-matrix ⋮ New error bounds for linear complementarity problems for \(B^S\)-matrices ⋮ A new upper bound for \(\|A^{-1}\|\) of a strictly \(\alpha\)-diagonally dominant \(M\)-matrix ⋮ Schur complement-based infinity norm bounds for the inverse of SDD matrices ⋮ An upper bound for \(\| A^{-1} \|_\infty \) of strictly diagonally dominant \(M\)-matrices ⋮ Estimation of \(\| A^{-1}\| _\infty \) for weakly chained diagonally dominant \(M\)-matrices ⋮ Linear system based approach for solving some related problems of \(M\)-matrices ⋮ Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems ⋮ Note on error bounds for linear complementarity problems for \(B\)-matrices

Cites Work

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• Lower bounds for the minimum eigenvalue of Hadamard product of an \(M\)-matrix and its inverse
• An inequality for the Hadamard product of an M-matrix and an inverse M- matrix
• A lower bound for the smallest singular value of a matrix
• A Hadamard product involving N-matrices
• On Two-Sided Bounds Related to Weakly Diagonally Dominant M-Matrices with Application to Digital Circuit Dynamics
• A Sufficient Condition for Nonvanishing of Determinants

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