The new improved estimates of the dominant degree and disc theorem for the Schur complement of matrices. (English) Zbl 1380.65071
The properties of the Schur complement and inequality techniques are used in this paper and provide new estimates of the diagonally, \(\gamma\)-diagonally and product \(\gamma\)-diagonally dominant degree on the Schur complement of matrices theory. The improvement of the obtained results has a major influence on the scientific areas of matrix and control theory, the computational mathematics and statistics. Distributions for the eigenvalues of the Schur complements are presented, as an application of the results, while a representative numerical example demonstrates the advantages of the proposed approximations.
Reviewer: Vasilis Dimitriou (Chania)
MSC:
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 15A06 | Linear equations (linear algebraic aspects) |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A45 | Miscellaneous inequalities involving matrices |
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
Keywords:
Schur complement; diagonally dominant matrix; dominant degree; eigenvalue distribution; numerical exampleReferences:
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