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Journals and Conferences
We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, which allows the simultaneous approximation of the extreme solutions of the matrix equations X +A∗X−1A = Q and X −A∗X−1A = Q. The algorithm is based on the cyclic reduction method.
We analyze the problem of the numerical solution of structured Markov chains encountered in queuing models: we describe the main computational problems and present the most advanced algorithms currently available for their solutions.
This paper provides an accurate model of the General Packet Radio Service (GPRS). GPRS is modeled as a single server queue in a Markovian environment. The queueing performance of data packets is evaluated by matrix geometric methods. The arrival process is assumed to follow a two state Markov modulated Poisson process (MMPP), and the service rate fluctuates… (More)
New theoretical results are presented about the principal matrix pth root. In particular, we show that the pth root is related to the matrix sign function and to the Wiener–Hopf factorization, and that it can be expressed as an integral over the unit circle. These results are used in the design and analysis of several new algorithms for the numerical… (More)
Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible M -matrix M are considered. The emphasis is on the case where M is an irreducible singular M -matrix, which arises in the study of Markov models. The doubling algorithm is considered for finding the minimal nonnegative solution, the one of practical… (More)
Society for induStrial and applied MatheMaticS Numerical Solution of Algebraic Riccati Equations Dario A. Bini, Bruno Iannazzo, and Beatrice Meini Fundamentals of Algorithms 9 This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a… (More)