The Newton-Shamanskii method for solving a quadratic matrix equation arising in quasi-birth-death problems
Numerical Analysis
2014-06-05 v1
Abstract
In order to determine the stationary distribution for discrete time quasi-birth-death Markov chains, it is necessary to find the minimal nonnegative solution of a quadratic matrix equation. We apply the Newton-Shamanskii method for solving the equation. We show that the sequence of matrices generated by the Newton-Shamanskii method is monotonically increasing and converges to the minimal nonnegative solution of the equation. Numerical experiments show the effectiveness of our method.
Keywords
Cite
@article{arxiv.1406.1075,
title = {The Newton-Shamanskii method for solving a quadratic matrix equation arising in quasi-birth-death problems},
author = {Peichang Guo},
journal= {arXiv preprint arXiv:1406.1075},
year = {2014}
}