IJPAM: Volume 7, No. 4 (2003)

SOME APPLICATIONS OF THE CRITERIA FOR
GENERALIZED DIAGONALLY DOMINANT MATRICES

Lei Li
Faculty of Engineering
Hosei University
Koganei, Tokyo 184-8584, JAPAN
e-mail: lilei@k.hosei.ac.jp


Abstract.We have proposed a new efficient algorithm to determine a positive diagonal matrix $D$ if matrix $A$ is a generalized diagonally dominant matrix, where $AD$ is a strictly diagonally dominant matrix [5]. In this paper, we show a Gauss form of this method, and by using this algorithm, we further propose some applications for distinguishing the symmetric positive definite matrices, M-matrices, the stability of nonlinear autonomous systems, computing the stable quantity of an real matrix, and estimating distribution of eigenvalues for generalized diagonally dominant matrices, etc.

Received: December 5, 2002

AMS Subject Classification: 47A67

Key Words and Phrases: criteria, positive definite, M-matrix, stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 4