A Generalised CRI Iteration Method for Complex Symmetric Linear Systems

Chen, Yunying Huang Guoliang

doi:10.4208/eajam.120518.231218

Cited by 3 publications

(1 citation statement)

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“…Complex nonsymmetric algebraic Riccati equations (NAREs) arise in many applied fields, such as the transient analysis of Markov modulated fluid flow model [23], openloop Nash equilibrium of linear quadratic differential games [13], applied probability [11] and transport theory [15], and other applications [20,24]. Here we consider a Markov modulated fluid flow {(F (t), J(t)) : t ≥ 0}, where F (t) and J(t) denote the fluid level in a container and the state of a Markov chain modulating the fluid process at time t, respectively.…”

Section: Introductionmentioning

confidence: 99%

A Parameterized Class of Complex Nonsymmetric Algebraic Riccati Equations

Dong¹

2021

NMTMA

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In this paper, by introducing a definition of parameterized comparison matrix of a given complex square matrix, the solvability of a parameterized class of complex nonsymmetric algebraic Riccati equations (NAREs) is discussed. The existence and uniqueness of the extremal solutions of the NAREs is proved. Some classical numerical methods can be applied to compute the extremal solutions of the NAREs, mainly including the Schur method, the basic fixed-point iterative methods, Newton's method and the doubling algorithms. Furthermore, the linear convergence of the basic fixed-point iterative methods and the quadratic convergence of Newton's method and the doubling algorithms are also shown. Moreover, some concrete parameter selection strategies in complex number field for the doubling algorithms are also given. Numerical experiments demonstrate that our numerical methods are effective.

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