Entrywise perturbation theory and error analysis for Markov chains
\textit{W. K. Grassmann}, \textit{M. I. Taksar} and \textit{D. P. Heyman} [Oper. Res. 33, 1107-1116 (1985; Zbl 0576.60083)] introduced a variant of Gaussian elimination for computing the steady-state vector of a Markov chain. The present author proves that their algorithm is stable, and that the problem itself is well-conditioned. The key to the analysis is to focus on entrywise relative error in both the data and the computed solution.
scientific article; zbMATH DE number 569120
scientific article