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arXiv · 1406.1075

The Newton-Shamanskii method for solving a quadratic matrix equation arising in quasi-birth-death problems

Peichang Guo
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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. 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.

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Peichang Guo. 2014-06-04. The Newton-Shamanskii method for solving a quadratic matrix equation arising in quasi-birth-death problems. https://arxiv.org/abs/1406.1075

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