Entrywise perturbation theory for diagonally dominant M-matrices with applications

摘要: This paper introduces a new perspective on the study of computational problems related to diagonally dominant M-matrices by establishing some entrywise perturbation results. If M-matrix is perturbed in way that each off-diagonal entry and its row sums (i.e. quantities diagonal dominance) have small relative errors, we show determinant, cofactors, inverse smallest eigenvalue all errors. The error bounds are given they do not depend any condition number. Applying this result studies electrical circuits tail probabilities queue whose embedded Markov chains GI/M/1 type, discuss sensitivity operating speed percentile length, respectively.