The Schur complement of strictly doubly diagonally dominant matrices and its application

DOI10.1016/j.laa.2012.02.001zbMath1248.15018OpenAlexW1981072042MaRDI QIDQ417572

Jianzhou Liu, Juan Zhang, Yu Liu

Publication date: 14 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.02.001

zbMATH Keywords

Schur complementBrauer ovals of Cassinilarge scale linear systemsinfinity normdominant degreedoubly diagonally dominant matrixSchur-based iteration

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) Miscellaneous inequalities involving matrices (15A45) Iterative numerical methods for linear systems (65F10)

Related Items (12)

On Schur complements of Dashnic–Zusmanovich type matrices ⋮ Upper norm bounds for the inverse of locally doubly strictly diagonally dominant matrices with its applications in linear complementarity problems ⋮ The doubly diagonally dominant degree of the Schur complement of strictly doubly diagonally dominant matrices and its applications ⋮ The improved disc theorems for the Schur complements of diagonally dominant matrices ⋮ The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications ⋮ An infinity norm bound for the inverse of strong \(\mathrm{SDD}_1\) matrices with applications ⋮ The Schur complement of \(\gamma\)-dominant matrices ⋮ Upper bounds for \(\Vert{} A^{-1}Q \Vert{}_\infty \) ⋮ Diagonal-Schur complements of Nekrasov matrices ⋮ Schur complement-based infinity norm bounds for the inverse of \(DSDD\) matrices ⋮ Schur complement-based infinity norm bounds for the inverse of SDD matrices ⋮ Several criteria for judgingH- and non-H-matrices

Cites Work

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• Invariance of the Brauer diagonal dominance in Gaussian elimination
• The Schur complements of \(\gamma\)-diagonally and product \(\gamma\)-diagonally dominant matrix and their disc separation
• The dominant degree and disc theorem for the Schur complement of matrix
• Inverse M-matrices
• Some interlacing properties of the Schur complement of a Hermitian matrix
• A lower bound for the smallest singular value of a matrix
• Some inequalities for singular values and eigenvalues of generalized Schur complements of products of matrices
• Doubly diagonally dominant matrices
• A minimum principle and estimates of the eigenvalues for Schur complements of positive semidefinite Hermitian matrices
• The Schur complements of generalized doubly diagonally dominant matrices
• Some properties on Schur complements of H-matrices and diagonally dominant matrices
• On Schur complement of block diagonally dominant matrices
• Upper bounds for the infinity norm of the inverse of SDD and \(\mathcal S\)-SDD matrices
• Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices
• Schur complements of diagonally dominant matrices
• H/sub ∞/ design with pole placement constraints: an LMI approach
• Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds

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