The Disc Theorem for the Schur Complement of Two Class Submatrices with $γ$-Diagonally Dominant Properties
Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.y14034
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 1 : pp. 84–97
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14