On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital circuit dynamics

P. N. Shivakumar, Joseph J. Williams, Qiang Ye, Corneliu A. Marinov

Research output: Contribution to journalArticlepeer-review

52 Citations (SciVal)

Abstract

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.

Original languageEnglish
Pages (from-to)298-312
Number of pages15
JournalSIAM Journal on Matrix Analysis and Applications
Volume17
Issue number2
DOIs
StatePublished - Apr 1996

Keywords

  • Bounds
  • Digital circuit dynamics
  • M-matrix
  • Weakly diagonally dominant matrix

ASJC Scopus subject areas

  • Analysis

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