
A computational framework for twodimensional random walks with restarts
The treatment of twodimensional random walks in the quarter plane leads...
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Rational Krylov and ADI iteration for infinite size quasiToeplitz matrix equations
We consider a class of linear matrix equations involving semiinfinite m...
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A family of fast fixed point iterations for M/G/1type Markov chains
We consider the problem of computing the minimal nonnegative solution G ...
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Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes
Markovmodulated Lévy processes lead to matrix integral equations of the...
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On partially homogeneous nearestneighbour random walks in the quarter plane and their application in the analysis of twodimensional queues with limited statedependency
This work deals with the stationary analysis of twodimensional partiall...
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Iterative and doubling algorithms for Riccatitype matrix equations: a comparative introduction
We review a family of algorithms for Lyapunov and Riccatitype equation...
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On the Solution of the Nonsymmetric TRiccati Equation
The nonsymmetric TRiccati equation is a quadratic matrix equation where...
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Solving quadratic matrix equations arising in random walks in the quarter plane
Quadratic matrix equations of the kind A_1X^2+A_0X+A_1=X are encountered in the analysis of QuasiBirthDeath stochastic processes where the solution of interest is the minimal nonnegative solution G. In many queueing models, described by random walks in the quarter plane, the coefficients A_1,A_0,A_1 are infinite tridiagonal matrices with an almost Toeplitz structure. Here, we analyze some fixed point iterations, including Newton's iteration, for the computation of G and introduce effective algorithms and acceleration strategies which fully exploit the Toeplitz structure of the matrix coefficients and of the current approximation. Moreover, we provide a structured perturbation analysis for the solution G. The results of some numerical experiments which demonstrate the effectiveness of our approach are reported.
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