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Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems

Published online by Cambridge University Press:  16 July 2018

Pei-Chang Guo
Pei-Chang Guo*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China.
*
*Corresponding author.Email address:gpeichang@126.com
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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. 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.

Keywords

65F3065H10Quadratic matrix equationquasi-birth-death problemsNewton-Shamanskii methodminimal nonnegative solution
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 4 , November 2014 , pp. 386 - 395
Copyright
Copyright © Global-Science Press 2014

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