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The Disc Theorem for the Schur Complement of Two Class Submatrices with γ-Diagonally Dominant Properties

Part of: Basic linear algebra

Published online by Cambridge University Press:  20 February 2017

Guangqi Li ,
Jianzhou Liu  and
Juan Zhang
Guangqi Li*
Affiliation:
Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
Jianzhou Liu*
Affiliation:
Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
Juan Zhang*
Affiliation:
Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China College of Science, National University of Defense Technology, Changsha, Hunan 410073, China
*
*Corresponding author. Email addresses:liujz@xtu.edu.cn (J.-Z. Liu), zhangjuan@xtu.edu.cn (J. Zhang)
*Corresponding author. Email addresses:liujz@xtu.edu.cn (J.-Z. Liu), zhangjuan@xtu.edu.cn (J. Zhang)
*Corresponding author. Email addresses:liujz@xtu.edu.cn (J.-Z. Liu), zhangjuan@xtu.edu.cn (J. Zhang)
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Abstract

The distribution for eigenvalues of Schur complement of matrices plays an important role in many mathematical problems. In this paper, we firstly present some criteria for H-matrix. Then as application, for two class matrices whose submatrices are γ-diagonally dominant and product γ-diagonally dominant, we show that the eigenvalues of the Schur complement are located in the Geršgorin discs and the Ostrowski discs of the original matrices under certain conditions.

Keywords

Schur complementGeršgorin TheoremOstrowski TheoremH-matrix

MSC classification

Secondary: 15A24: Matrix equations and identities
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017 , pp. 84 - 97
Copyright
Copyright © Global-Science Press 2017 

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References

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