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A Modified Gradient Based Algorithm for Solving Matrix Equations AXB + CXTD = F

Author

Listed:
  • Kanmin Wang
  • Zhibing Liu
  • Chengfeng Xu

Abstract

In this paper, we develop a modified gradient based algorithm for solving matrix equations AXB + CXTD = F. Different from the gradient based method introduced by Xie et al., 2010, the information generated in the first half‐iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:954523
    DOI: 10.1155/2014/954523
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    References listed on IDEAS

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    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. 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).
    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).

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