Complex Nonsymmetric Algebraic Riccati Equations Arising in Markov Modulated Fluid Flows

Abstract

Motivated by the transient analysis of stochastic fluid flow models, we introduce a class of complex nonsymmetric algebraic Riccati equations. The existence and uniqueness of the extremal solutions to these equations are proved. The extremal solutions can be computed by Newton's method and some fixed-point iterative schemes. Criteria for choosing parameters are suggested such that three existing doubling algorithms---SDA of Guo, Lin, and Xu [Numer. Math., 103 (2006), pp. 393--412], SDA-ss of Bini, Meini, and Poloni [Numer. Math., 116 (2010), pp. 553--578], and ADDA of W.-G. Wang, W.-C. Wang, and R.-C. Li [SIAM J. Matrix Anal. Appl., 33 (2012), pp. 170--194] can also deliver the extremal solutions.