Blockwise perturbation theory for block \(p\)-cyclic stochastic matrices (Q1968790)

Let \(P\) be a block \(p\)-cyclic stochastic matrix with stationary distribution correspondingly partitioned as \(\pi^T:=(\pi_1^T, \dots, \pi_p^T)\). The article establishes the relative error bound for \(\pi_i^T\) when each block of \(P\) receives a small relative perturbation, generalizing a result of \textit{G. Stewart} [Numer. Math. 65, No. 1, 135-141 (1993; Zbl 0797.15019)].