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An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations

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  • Ying Zhang
  • Ai-Guo Wu
  • Hui-Jie Sun

Abstract

In this paper, an implicit iterative algorithm is proposed for solving a class of Lyapunov matrix equations arising in Itô stochastic linear systems. A tuning parameter is introduced in this algorithm, and thus the convergence rate of the algorithm can be changed. Some conditions are presented such that the developed algorithm is convergent. In addition, an explicit expression is also derived for the optimal tuning parameter, which guarantees that the obtained algorithm achieves its fastest convergence rate. Finally, numerical examples are employed to illustrate the effectiveness of the given algorithm.

Suggested Citation

  • Ying Zhang & Ai-Guo Wu & Hui-Jie Sun, 2018. "An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(2), pages 425-434, January.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:2:p:425-434
    DOI: 10.1080/00207721.2017.1407009
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    Cited by:

    1. Wu, Ai-Guo & Sun, Hui-Jie & Zhang, Ying, 2018. "Two iterative algorithms for stochastic algebraic Riccati matrix equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 410-421.

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