TY - JOUR
T1 - A Parameterized Class of Complex Nonsymmetric Algebraic Riccati Equations
AU - Dong , Liqiang
AU - Li , Jicheng
AU - Liu , Xuenian
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 650
EP - 691
PY - 2021
DA - 2021/06
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2019-0140
UR - https://global-sci.org/intro/article_detail/nmtma/19193.html
KW - Complex nonsymmetric algebraic Riccati equation, extremal solution, numerical
method, doubling algorithm, complex parameter selection strategy.
AB - <p style="text-align: justify;">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&#39;s method and the doubling algorithms. Furthermore, the linear convergence
of the basic fixed-point iterative methods and the quadratic convergence of Newton&#39;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.</p>