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Volume 4, Issue 4
Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems

Pei-Chang Guo

DOI: 10.4208/eajam.040914.301014a

East Asian J. Appl. Math., 4 (2014), pp. 386-395.

Published online: 2018-02

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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

Quadratic matrix equation, quasi-birth-death problems, Newton-Shamanskii method, minimal nonnegative solution.

  • AMS Subject Headings

65F30, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-386, author = {Pei-Chang Guo}, title = {Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {4}, pages = {386--395}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.040914.301014a}, url = {http://global-sci.org/intro/article_detail/eajam/10846.html} }
TY - JOUR T1 - Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems AU - Pei-Chang Guo 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 -

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.

Pei-Chang Guo. (2018). Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems. East Asian Journal on Applied Mathematics. 4 (4). 386-395. doi:10.4208/eajam.040914.301014a
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