The Schur complements of \(\gamma\)-diagonally and product \(\gamma\)-diagonally dominant matrix and their disc separation

DOI10.1016/j.laa.2009.10.021zbMath1186.15016OpenAlexW1964164355MaRDI QIDQ846342

Jianzhou Liu, Ze-Jun Huang

Publication date: 9 February 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.10.021

zbMATH Keywords

eigenvalueSchur complementM-matrixH-matrixGerschgorin theoremdiagonally dominant matrixdominant degreeBrauer theorem

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48) Iterative numerical methods for linear systems (65F10)

Related Items (14)

On Schur complements of Dashnic–Zusmanovich type matrices ⋮ The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices ⋮ 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 ⋮ On Cvetković-Kostić-Varga type matrices ⋮ The Schur complement of \(\gamma\)-dominant matrices ⋮ The Schur complement of strictly doubly diagonally dominant matrices and its application ⋮ Scaling technique for partition-Nekrasov matrices ⋮ Properties for the Perron complement of three known subclasses of \(H\)-matrices ⋮ The estimates of diagonally dominant degree and eigenvalues distributions for the Schur complements of matrices ⋮ Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems ⋮ The new improved estimates of the dominant degree and disc theorem for the Schur complement of matrices ⋮ On Schur complements of Cvetković-Kostić-Varga type matrices

Cites Work

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• Invariance of the Brauer diagonal dominance in Gaussian elimination
• Inverse M-matrices
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• Some inequalities for singular values and eigenvalues of generalized Schur complements of products of matrices
• Doubly diagonally dominant matrices
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• The Schur complement and its applications
• The Schur complements of generalized doubly diagonally dominant matrices
• Some properties on Schur complements of H-matrices and diagonally dominant matrices
• Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices
• Schur complements of diagonally dominant matrices
• Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds

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