It is explained how the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix can be found by the Schur method and compared with Newton's method and basic fixed-point iterations.Expand

Newton's method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation andumerical results are reported to illustrate the convergence behaviour of various algorithms.Expand

Newton's method and a class of basic fixed-point iterations can be used to find its minimal positive solution whenever it has a positive solution of any equation in this class of nonsymmetric algebraic Riccati equations.Expand

The Latouche-Ramaswami algorithm, combined with a shift technique suggested by He, Meini, and Rhee, is breakdown-free and is able to find the minimal solution more efficiently and more accurately than the algorithm without a shift.Expand

Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible singular $M$-matrix, which arises in the study of Markov models, are considered.Expand

Newtonâ€™s method for the inverse matrix pth root, Aâˆ’1/p, has the attraction that it involves only matrix multiplication. We show that if the starting matrix is cI for c âˆˆ R then the iterationâ€¦ Expand

The linear convergence appears to be dominant, and the efficiency of the Newton iteration can be improved significantly by applying a double Newton step at the right time.Expand

An efficient algorithm is obtained that identifies and solves a hyperbolic or overdamped QEP maintaining symmetry throughout and guaranteeing real computed eigenvalues.Expand

It is shown that a relatively efficient test forhyperbolicity can be obtained by computing the eigenvalues of the QEP, and that a hyperbolic QEP is overdamped if and only if its largest eigenvalue is nonpositive.Expand