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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 5, 2015

The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices

  • Feng Wang and Deshu Sun
From the journal Open Mathematics

Abstract

The theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-block strictly diagonally dominant matrices and I(II)-block strictly doubly diagonally dominant matrices are obtained, which improve some relative results in Liu [Linear Algebra Appl. 435(2011) 3085-3100]. 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.

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Received: 2015-5-8
Accepted: 2015-10-14
Published Online: 2015-11-5

©2015 Feng Wang, Deshu Sun

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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