Computers & Mathematics with Applications
Convergence analysis of a variant of the Newton method for solving nonlinear equations
Computers & Mathematics with Applications
On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations
Computers & Mathematics with Applications
Alternating-directional Doubling Algorithm for $M$-Matrix Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
Departure process analysis of the multi-type MMAP[K]/PH[K]/1 FCFS queue
Performance Evaluation
The eigenvalue shift technique and its eigenstructure analysis of a matrix
Journal of Computational and Applied Mathematics
Loss rates for stochastic fluid models
Performance Evaluation
On the numerical solution of a structured nonsymmetric algebraic Riccati equation
Performance Evaluation
Monotone convergence of Newton-like methods for M-matrix algebraic Riccati equations
Numerical Algorithms
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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 interest. The algorithm has been recently studied by others for the case where $M$ is a nonsingular $M$-matrix. A shift technique is proposed to transform the original Riccati equation into a new Riccati equation for which the four coefficient matrices form a nonsingular matrix. The convergence of the doubling algorithm is accelerated when it is applied to the shifted Riccati equation.