| Abstract: | 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. |
