Algebraic Schwarz methods for the numerical solution of Markov chains
The authors propose an iterative method to solve singular linear systems. They use the additive and multiplicative Schwarz method to solve large sparse singular linear systems of the form \(Ax=b\), where \(A\) is a singular M-matrix, which means that \(A=I-B\) and \(B\) is nonnegative stochastic matrix. In particular, they consider the case \(b=0\), which corresponds to the stationary probability of a Markov chain represented by \(B\). They show that the multiplicative Schwarz iterations is convergent.
scientific article; zbMATH DE number 2081257
scientific article