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A Generalized HSS Iteration Method for Continuous Sylvester Equations

Author

Listed:
  • Xu Li
  • Yu-Jiang Wu
  • Ai-Li Yang
  • Jin-Yun Yuan

Abstract

Based on the Hermitian and skew‐Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non‐Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four‐parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the iterative process. An exact parameter region of convergence for the method is strictly proved and a minimum value for the upper bound of the iterative spectrum is derived. Moreover, to reduce the computational cost, we establish an inexact variant of the GHSS (IGHSS) iteration method whose convergence property is discussed. Numerical experiments illustrate the efficiency and robustness of the GHSS iteration method and its inexact variant.

Suggested Citation

  • Xu Li & Yu-Jiang Wu & Ai-Li Yang & Jin-Yun Yuan, 2014. "A Generalized HSS Iteration Method for Continuous Sylvester Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:578102
    DOI: 10.1155/2014/578102
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    References listed on IDEAS

    as
    1. Jituan Zhou & Ruirui Wang & Qiang Niu, 2012. "A Preconditioned Iteration Method for Solving Sylvester Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, July.
    2. Feng Yin & Guang-Xin Huang, 2012. "An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Deqin Chen & Feng Yin & Guang-Xin Huang, 2012. "An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB = E, CXD = F," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Feng Yin & Guang-Xin Huang, 2012. "An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-28, August.
    5. Jituan Zhou & Ruirui Wang & Qiang Niu, 2012. "A Preconditioned Iteration Method for Solving Sylvester Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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