Bordered Matrices, Singular Systems, and Ergodic Markov Chains

Abstract

Systems of linear equations involving submatrices of singular M-matrices have been considered in the calculation of stationary distribution vectors of ergodic Markov chains. In this paper, an alternative appproach is suggested, using bordered matrices instead, motivated by the stability analysis of the first approach. The conditioning of this approach, which applies to general as well as M-matrices, is considered. Two numerical examples with small matrices are included.