TY - JOUR
T1 - On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital circuit dynamics
AU - Shivakumar, P. N.
AU - Williams, Joseph J.
AU - Ye, Qiang
AU - Marinov, Corneliu A.
PY - 1996/4
Y1 - 1996/4
N2 - Let A be a real weakly diagonally dominant M-matrix. We establish upper and lower bounds for the minimal eigenvalue of A, for its corresponding eigenvector, and for the entries of the inverse of A. Our results are applied to find meaningful two-sided bounds for both the ℓ1-norm and the weighted Perron-norm of the solution x(t) to the linear differential system ẋ = -Ax, x(0) = x0 > 0. These systems occur in a number of applications, including compartmental analysis and RC electrical circuits. A detailed analysis of a model for the transient behaviour of digital circuits is given to illustrate the theory.
AB - Let A be a real weakly diagonally dominant M-matrix. We establish upper and lower bounds for the minimal eigenvalue of A, for its corresponding eigenvector, and for the entries of the inverse of A. Our results are applied to find meaningful two-sided bounds for both the ℓ1-norm and the weighted Perron-norm of the solution x(t) to the linear differential system ẋ = -Ax, x(0) = x0 > 0. These systems occur in a number of applications, including compartmental analysis and RC electrical circuits. A detailed analysis of a model for the transient behaviour of digital circuits is given to illustrate the theory.
KW - Bounds
KW - Digital circuit dynamics
KW - M-matrix
KW - Weakly diagonally dominant matrix
UR - http://www.scopus.com/inward/record.url?scp=0030556796&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030556796&partnerID=8YFLogxK
U2 - 10.1137/S0895479894276370
DO - 10.1137/S0895479894276370
M3 - Article
AN - SCOPUS:0030556796
SN - 0895-4798
VL - 17
SP - 298
EP - 312
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 2
ER -