TY - JOUR
T1 - Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 386
EP - 395
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.040914.301014a
UR - https://global-sci.org/intro/article_detail/eajam/10846.html
KW - Quadratic matrix equation, quasi-birth-death problems, Newton-Shamanskii method, minimal nonnegative solution.
AB - <p style="text-align: justify;">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. The Newton-Shamanskii method is applied to solve this
equation, and the sequence of matrices produced is monotonically increasing and converges to its minimal nonnegative solution. Numerical results illustrate the effectiveness of this procedure.</p>