Favati P., Meini B. On functional iteration methods for solving nonlinear matrix equations arising in queueing problems. Technical report, 1999. |

Abstract (English) |
The problem of the computation of the minimal nonnegative solution $G$ of the nonlinear matrix equation $X=sum_{i=0}^{+infty}X^iA_i$ is considered. This problem arises in the numerical solution of M/G/1 type Markov chains,where $A_i$, $ige0$, are nonnegative $ktimes k$ matrices such that $sum_{i=0}^{+infty}A_i$ is column stochastic. We analyze classical functional iteration methods, by estimating the rate of convergence, in relation with spectral properties of the starting approximation matrix $X_0$. Based on these new convergence results, we propose an effective method to choose a matrix $X_0$, which drastically reduces the number of iterations; the additional cost needed to compute $X_0$ is much less than the overall savings achieved by reducing the number of iterations. | |

Subject | G.1.0 General 65U05 Numerical methods in probability and statistics |

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