IJPAM: Volume 7, No. 4 (2003)
GENERALIZED DIAGONALLY DOMINANT MATRICES
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 if matrix
is a generalized diagonally dominant matrix,
where
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