The improved disc theorems for the Schur complements of diagonally dominant matrices

DOI10.1186/1029-242X-2013-2zbMath1279.15016WikidataQ59301954 ScholiaQ59301954MaRDI QIDQ389185

Gen Tu, Jianzhou Liu, Juan Zhang

Publication date: 17 January 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

eigenvalueSchur complementdiagonally dominant matricesGerschgorin theorem

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45)

Related Items (3)

The Schur complement of \(\gamma\)-dominant matrices ⋮ Some new inequalities for the Hadamard product of a nonsingularM-matrix and its inverse ⋮ The new improved estimates of the dominant degree and disc theorem for the Schur complement of matrices

Cites Work

• The Schur complement of strictly doubly diagonally dominant matrices and its application
• The Schur complements of \(\gamma\)-diagonally and product \(\gamma\)-diagonally dominant matrix and their disc separation
• A convergence analysis of block accelerated over-relaxation iterative methods for weak block \(H\)-matrices to partition \(\pi \)
• The dominant degree and disc theorem for the Schur complement of 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
• Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices
• Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds

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