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

TL;DR

This paper introduces an efficient iterative method using linear least squares for computing mean first passage times in ergodic Markov chains, demonstrating suitability for large sparse systems.

Contribution

The paper presents a novel linear least squares-based iterative scheme for calculating MFPTs, improving efficiency and accuracy over existing methods.

Findings

Method is suitable for large sparse systems

Numerical results show improved accuracy

Compared favorably with existing algorithms

Abstract

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.