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Low-Rank Methods for Solving Discrete-Time Projected Lyapunov Equations

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  • Yiqin Lin

    (School of Science, Hunan University of Science and Engineering, Yongzhou 425199, China)

Abstract

In this paper, we consider the numerical solution of large-scale discrete-time projected Lyapunov equations. We provide some reasonable extensions of the most frequently used low-rank iterative methods for linear matrix equations, such as the low-rank Smith method and the low-rank alternating-direction implicit (ADI) method. We also consider how to reduce complex arithmetic operations and storage when shift parameters are complex and propose a partially real version of the low-rank ADI method. Through two standard numerical examples from discrete-time descriptor systems, we will show that the proposed low-rank alternating-direction implicit method is efficient.

Suggested Citation

  • Yiqin Lin, 2024. "Low-Rank Methods for Solving Discrete-Time Projected Lyapunov Equations," Mathematics, MDPI, vol. 12(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1166-:d:1374876
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