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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
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.
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