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

Pei-Chang Guo


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

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  • Abstract

In order to determine the stationary distribution for discrete time quasi-birthdeath 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.

  • History

Published online: 2018-02

  • AMS Subject Headings

65F30, 65H10

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