Relaxed Fixed Point Iterations for Matrix Equations Arising in Markov Chains Modeling
Abstract
We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Markov chain. These variants derive from certain staircase regular splittings of the block Hessenberg M-matrix associated with the Markov chain. By exploiting the staircase profile we introduce a two-step fixed point iteration. The iteration can be further accelerated by computing a weighted average between the approximations obtained at two consecutive steps. The convergence of the basic two-step fixed point iteration and of its relaxed modification is proved. Our theoretical analysis, along with several numerical experiments show that the proposed variants generally outperform the classical iterations.
Cite
@article{arxiv.2205.13187,
title = {Relaxed Fixed Point Iterations for Matrix Equations Arising in Markov Chains Modeling},
author = {Luca Gemignani and Beatrice Meini},
journal= {arXiv preprint arXiv:2205.13187},
year = {2022}
}