Upper bounds for the infinity norm of the inverse of SDD and \(\mathcal S\)-SDD matrices
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Publication:2370680
DOI10.1016/j.cam.2006.08.013zbMath1123.15018OpenAlexW2079358656MaRDI QIDQ2370680
Publication date: 29 June 2007
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2006.08.013
Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)
Related Items (26)
Bounds on the \(l_\infty\) norm of inverses for certain block matrices ⋮ Upper norm bounds for the inverse of locally doubly strictly diagonally dominant matrices with its applications in linear complementarity problems ⋮ New subclasses of the class of \( \mathcal H \)-matrices and related bounds for the inverses ⋮ On block generalizations of \( \mathcal H \)-matrices ⋮ Error bounds for the linear complementarity problem with a \(\Sigma \)-SDD matrix ⋮ New error bounds for linear complementarity problems of \(\Sigma \)-SDD matrices and \(SB\)-matrices ⋮ An infinity norm bound for the inverse of strong \(\mathrm{SDD}_1\) matrices with applications ⋮ The Schur complement of \(\gamma\)-dominant matrices ⋮ The Schur complement of strictly doubly diagonally dominant matrices and its application ⋮ Upper bounds for \(\Vert{} A^{-1}Q \Vert{}_\infty \) ⋮ On \(\mathrm{SDD}_1\) matrices ⋮ Bounds for the inverses of generalized Nekrasov matrices ⋮ New classes of nonsingular matrices and upper bounds for their inverses ⋮ Some bounds for inverses involving matrix sparsity pattern ⋮ Max-norm bounds for the inverse of \(S\)-Nekrasov matrices ⋮ Error bounds for linear complementarity problems for \(SB\)-matrices ⋮ CKV-type matrices with applications ⋮ An infinity norm bound for the inverse of Dashnic-Zusmanovich type matrices with applications ⋮ Bounds for norms of the matrix inverse and the smallest singular value ⋮ Bounds for the infinity norm of the inverse for certain \(M\)- and \(H\)-matrices ⋮ Some new results on determinantal inequalities and applications ⋮ Schur complement-based infinity norm bounds for the inverse of SDD matrices ⋮ On Dashnic-Zusmanovich (DZ) and Dashnic-Zusmanovich type (DZT) matrices and their inverses ⋮ Error bounds for linear complementarity problems of \(MB\)-matrices ⋮ An improvement of the infinity norm bound for the inverse of \(\{P_1,P_2\}\)-Nekrasov matrices ⋮ A new lower bound for the smallest singular value
Cites Work
- Criteria for generalized diagonally dominant matrices and \(M\)-matrices
- A lower bound for the smallest singular value of a matrix
- On diagonal dominance arguments for bounding \(\| A^{-1}\|_\infty\)
- A new Geršgorin-type eigenvalue inclusion set
- Über die Determinanten mit überwiegender Hauptdiagonale
- Convergence Properties of the Spline Fit
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