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

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

From MaRDI portal
Publication:6252082

DOI10.4208/EAJAM.040914.301014AarXiv1406.1075MaRDI QIDQ6252082

Author name not available (Why is that?)

Publication date: 4 June 2014

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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