Abstract
The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α-diagonally and product α-diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.
Highlights
We know that A is called a strictly diagonally dominant matrix if aii > Ri ( A), ∀ i ∈ N
The Schur complement of matrix is an important part of matrix theory, which has been proved to be useful tools in many fields such as control theory, statistics and computational mathematics
We know that the Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices, and the Schur complements of Ostrowski matrices are Ostrowski matrices
Summary
We know that A is called a strictly diagonally dominant matrix if aii > Ri ( A), ∀ i ∈ N. (2015) The Estimates of Diagonally Dominant Degree and Eigenvalue Inclusion Regions for the Schur Complement of Matrices. ( ) ( ) ( ) = A β A A= (β ) A β − A β , β A(β ) −1 A β , β , is called the Schur complement of A with respect to A(β ).
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