Volume 10, Issue 1
The Disc Theorem for the Schur Complement of Two Class Submatrices with $γ$-Diagonally Dominant Properties

Guangqi Li, Jianzhou Liu & Juan Zhang

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 84-97.

Published online: 2017-10

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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 sub-matrices 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.

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@Article{NMTMA-10-84, author = {}, title = {The Disc Theorem for the Schur Complement of Two Class Submatrices with $γ$-Diagonally Dominant Properties}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {1}, pages = {84--97}, 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 sub-matrices 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.y14034}, url = {http://global-sci.org/intro/article_detail/nmtma/12337.html} }
TY - JOUR T1 - The Disc Theorem for the Schur Complement of Two Class Submatrices with $γ$-Diagonally Dominant Properties JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 84 EP - 97 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.y14034 UR - https://global-sci.org/intro/article_detail/nmtma/12337.html KW - AB -

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 sub-matrices 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.

Guangqi Li, Jianzhou Liu & Juan Zhang. (2020). The Disc Theorem for the Schur Complement of Two Class Submatrices with $γ$-Diagonally Dominant Properties. Numerical Mathematics: Theory, Methods and Applications. 10 (1). 84-97. doi:10.4208/nmtma.2017.y14034
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