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Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations

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  • Hongcai Yin
  • Huamin Zhang

Abstract

By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations and in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation . The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm.

Suggested Citation

  • Hongcai Yin & Huamin Zhang, 2014. "Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, June.
    • Handle: RePEc:hin:jnlmpe:831321
    DOI: 10.1155/2014/831321
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