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PHSS Iterative Method for Solving Generalized Lyapunov Equations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shi-Yu Li & Hai-Long Shen & Xin-Hui Shao, 2019. "PHSS Iterative Method for Solving Generalized Lyapunov Equations," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:38-:d:194640
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