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A Preconditioned Iteration Method for Solving Sylvester Equations

Author

Listed:
  • Jituan Zhou
  • Ruirui Wang
  • Qiang Niu

Abstract

A preconditioned gradient‐based iterative method is derived by judicious selection of two auxil‐ iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient‐based iterative method.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:401059
    DOI: 10.1155/2012/401059
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    References listed on IDEAS

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    1. M. Y. Waziri & W. J. Leong & M. Mamat, 2012. "A Two‐Step Matrix‐Free Secant Method for Solving Large‐Scale Systems of Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. M. Y. Waziri & W. J. Leong & M. Mamat, 2012. "A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, March.
    3. Danny C. Sorensen & Yunkai Zhou, 2003. "Direct methods for matrix Sylvester and Lyapunov equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2003(6), pages 277-303.
    4. Danny C. Sorensen & Yunkai Zhou, 2003. "Direct methods for matrix Sylvester and Lyapunov equations," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-27, January.
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    Cited by:

    1. F. Toutounian & D. Khojasteh Salkuyeh & M. Mojarrab, 2015. "LSMR Iterative Method for General Coupled Matrix Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    2. Ovgu Cidar Iyikal, 2022. "Numerical Solution of Sylvester Equation Based on Iterative Predictor‐Corrector Method," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    3. 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).
    4. Kanmin Wang & Zhibing Liu & Chengfeng Xu, 2014. "A Modified Gradient Based Algorithm for Solving Matrix Equations AXB + CXTD = F," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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