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

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

Mathematics, 2024, vol. 12, issue 8, 1-20

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.

Keywords: discrete-time projected Lyapunov equation; Smith method; ADI method; low-rank method; matrix pencil; D-stable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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