Year: 2021
Author: Jicheng Li, Xuenian Liu, Liqiang Dong, Jicheng Li, Xuenian Liu
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 650–691
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0140
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 650–691
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 42
Keywords: Complex nonsymmetric algebraic Riccati equation extremal solution numerical method doubling algorithm complex parameter selection strategy.