Linear least square method for the computation of the mean first passage times of ergodic markov chains

An efficient and accurate iterative scheme for the computation of the mean first passage times (MFPTs) of ergodic Markov chains has been presented. Firstly, the computation problem of MFPTs is transformed into a set of linear equations. It has been proven that each of these equations is compatible and their minimal norm solutions constitute MFPTs. A new presentation of the MFPTs is also derived. Using linear least square algorithms, some numerical examples compared with the finite algorithm of Hunter [LAA, 549(2018)100-122] and iterative algorithm of J.Xu [AMC, 250(2025)372-389] are given. These results show that the new algorithm is suitable for large sparse systems.