Title of article :
The Schur Complement of γ-Dominant Matrices
Author/Authors :
Zhou ، Lixin Department of Mathematics - School of Science - Guilin University of Aerospace Technology , Lyu ، Zhen-Hua Department of Mathematics - School of Science - Shenyang Aerospace University , Liu ، Jianzhou Department of Mathematics - School of Mathematics and Computational Science - Xiangtan Universit
From page :
3701
To page :
3725
Abstract :
In this paper, we present the γ (product γ )-diagonally dominant degree on the Schur complement of γ (product γ )-diagonally dominant matrices. Consequently, the disc theorems for the Schur complement of γ (product γ )-diagonally dominant matrices are obtained using the diagonally dominant degree on Schur complements, which improves and extends some related results. Further, to solve large-scale linear systems, we give the spectral radius estimates for the inverse matrices of γ (product γ )-diagonally dominant matrices and their Schur complements. When the coefficient matrix of linear system is γ (product γ )-diagonally dominant matrix, according to the special properties and the structures of γ (product γ )-diagonally dominant matrices, we design a class of special iteration for solving equations. Combining the spectral iteration with the Schur-based iterative method, we obtain a new iterative method called the Schur-based inverse algorithm, which reduces the order of the matrix and has a good convergence. The numerical examples are given to verify the validity of our results.
Keywords :
Schur complement , H , matrix , Disc theorem , Diagonally dominant matrices , Eigenvalue
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
Record number :
2775204
Link To Document :
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