Heyman, Daniel P.; Reeves, Alyson Numerical solution of linear equations arising in Markov chain models. (English) Zbl 0757.65156 ORSA J. Comput. 1, No. 1, 52-60 (1989). The authors examine several non-iterative methods for numerically solving the linear equation \(x=b+Qx\) that arises in the study of Markov chains. Here \(b\) is a vector of nonnegative constants and \(Q\) is a substochastic (not necessarily sparse) matrix, derived from a stochastic by deleting state 0.The emphasis is done on moments of first-passage times and times to absorption. A comparison of methods on the basis of accuracy and computation leads to the conclusion that state-reduction is the most accurate and that the matrix solutions need the least computational time. Reviewer: I.S.Molchanov (Kiev) Cited in 12 Documents MSC: 65C99 Probabilistic methods, stochastic differential equations 65F05 Direct numerical methods for linear systems and matrix inversion 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:substochastic matrix; non-iterative methods; Markov chains; first-passage times; comparison of methods; state-reduction PDFBibTeX XMLCite \textit{D. P. Heyman} and \textit{A. Reeves}, ORSA J. Comput. 1, No. 1, 52--60 (1989; Zbl 0757.65156) Full Text: DOI