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The Estimates of Diagonally Dominant Degree and Eigenvalue Inclusion Regions for the Schur Complement of Matrices
Department of Mathematics, Heze University, Shandong, China
- 1 Department of Mathematics, Heze University, Shandong, China
Advances in Pure Mathematics·Volume 05 (2015)·Pages 643–652·Published 12 August 2015·DOI10.4236/apm.2015.510058
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Abstract
The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α -diagonally and product α -diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. 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.
KeywordsSchur ComplementGerschgorin TheoremDiagonally Dominant DegreeEigenvalue
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