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Journal of Applied Mathematics
Volume 2013, Article ID 973152, 10 pages
http://dx.doi.org/10.1155/2013/973152
Research Article

The Diagonally Dominant Degree and Disc Separation for the Schur Complement of Ostrowski Matrix

1School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, China
2Department of Mathematics, Heze University, Heze, Shandong 274015, China

Received 25 April 2013; Accepted 31 August 2013

Academic Editor: Kazutake Komori

Copyright © 2013 Jianxing Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By applying the properties of Schur complement and some inequality techniques, some new estimates of diagonally and doubly diagonally dominant degree of the Schur complement of Ostrowski matrix are obtained, which improve the main results of Liu and Zhang (2005) and Liu et al. (2012). As an application, we present new inclusion regions for eigenvalues of the Schur complement of Ostrowski matrix. In addition, a new upper bound for the infinity norm on the inverse of the Schur complement of Ostrowski matrix is given. Finally, we give numerical examples to illustrate the theory results.