PHSS Iterative Method for Solving Generalized Lyapunov Equations

Shi-Yu Li, Hai-Long Shen and Xin-Hui Shao
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Shi-Yu Li: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
Hai-Long Shen: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
Xin-Hui Shao: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China

Mathematics, 2019, vol. 7, issue 1, 1-13

Abstract: Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

Keywords: Lyapunov equation; HSS iterative method; PHSS iterative method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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