Linear system based approach for solving some related problems of \(M\)-matrices

DOI10.1016/j.laa.2009.08.011zbMath1205.15008OpenAlexW1984409797WikidataQ60513624 ScholiaQ60513624MaRDI QIDQ1044610

Ting-Zhu Huang, Jin-Liang Shao, Guo-Feng Zhang

Publication date: 18 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.08.011

zbMATH Keywords

linear systemdiagonal dominanceM-matrixinfinity normSkeel condition number

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Linear equations (linear algebraic aspects) (15A06) Conditioning of matrices (15A12)

Cites Work

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• An iterative algorithm for searching a scaling matrix for diagonal dominance
• Estimation of \(\| A ^{-1} \|_\infty \) and the smallest singular value
• Bounds for norms of the matrix inverse and the smallest singular value
• The infinity norm bound for the inverse of nonsingular diagonal dominant matrices
• An upper bound for \(\| A^{-1}\|_{\infty}\) of strictly diagonally dominant \(M\)-matrices
• Strict Diagonal Dominance and Optimal Bounds for the Skeel Condition Number
• Scaled Pivots and Scaled Partial Pivoting Strategies
• On Two-Sided Bounds Related to Weakly Diagonally Dominant M-Matrices with Application to Digital Circuit Dynamics

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