A structured doubling algorithm for nonsymmetric algebraic Riccati equations (a singular case)

In this paper we propose a structured doubling algorithm (SDA) for the computation of the minimal nonnegative solutions to the nonsymmetric algebraic Riccati equation (NARE) and its dual equation simultaneously, for a singular case. Similar to the Newton’s method we establish a global and linear convergence for SDA under the singular condition, using only elementary matrix theory. Numerical experiments show that the SDA algorithm is feasible and eective, outperforms Newton’s method for NARE. Furthermore, SDA algorithm can easily be applied to solving the quadratic matrix equation, arising form quasi-birth-death (QBD) processes, which is dierent from the existing Latouchu-Ramaswami (LR) algorithm. The convergence of SDA is shown to be linear at least with rate 1 when QBD is null recurrent.

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