A Shifted Cyclic Reduction Algorithm for Quasi-Birth-Death Problems
نویسندگان
چکیده
A shifted cyclic reduction algorithm has been proposed by He, Meini, and Rhee [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 673–691] for finding the stochastic matrix G associated with discrete-time quasi-birth-death (QBD) processes. We point out that the algorithm has quadratic convergence even for null recurrent QBDs. We also note that the approximations (to the matrix G) obtained by their algorithm are always stochastic when they are nonnegative.
منابع مشابه
Convergence Rate of the Cyclic Reduction Algorithm for Null Recurrent Quasi-Birth-Death Problems
The minimal nonnegative solution G of the matrix equation G = A 0 + A 1 G + A 2 G 2 , where the matrices A 0 , A 1 and A 2 are nonnegative and A 0 + A 1 + A 2 is stochastic, plays an important role in the study of quasi-birth-death processes (QBDs). The cyclic reduction algorithm is a very efficient iteration for finding the matrix G, under the standard assumption that the transition probabilit...
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ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 23 شماره
صفحات -
تاریخ انتشار 2002