Bounds for norms of the matrix inverse and the smallest singular value

DOI10.1016/j.laa.2007.12.026zbMath1157.15025OpenAlexW2042782097MaRDI QIDQ952048

Nenad Morača

Publication date: 6 November 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.12.026

zbMATH Keywords

upper boundssingular valueslower bounds\(M\)-matricesdiagonal dominance\(H\)-matricesmatrix norms

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Numerical computation of matrix norms, conditioning, scaling (65F35)

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Cites Work

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• Some simple estimates for singular values of a matrix
• A Gershgorin-type lower bound for the smallest singular value
• A lower bound for the smallest singular value of a matrix
• On diagonal dominance arguments for bounding \(\| A^{-1}\|_\infty\)
• Further lower bounds for the smallest singular value
• Upper bounds for the infinity norm of the inverse of SDD and \(\mathcal S\)-SDD matrices
• Convergence Properties of the Spline Fit
• Monotonicity and Discretization Error Estimates

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