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Finite iterative algorithms for the generalized Sylvester-conjugate matrix equation \({AX+BY=E\overline{X}F+S}\)

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Abstract

This paper investigates the generalized Sylvester-conjugate matrix equation, which includes the normal Sylvester-conjugate, Kalman–Yakubovich-conjugate and generalized Sylvester matrix equations as its special cases. An iterative algorithm is presented for solving such a kind of matrix equations. This iterative method can give an exact solution within finite iteration steps for any initial values in the absence of round-off errors. Another feature of the proposed algorithm is that it is implemented by original coefficient matrices. By specifying the proposed algorithm, iterative algorithms for some special matrix equations are also developed. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

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Authors and Affiliations

  1. Information and Control Research Center, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, 518055, People’s Republic of China

    Ai-Guo Wu

  2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Ai-Guo Wu, Guang-Ren Duan & Yan-Ming Fu

  3. National Key Laboratory of Antennas and Microwave Technology, Xidian University, Xi’an, 710071, People’s Republic of China

    Wei-Jun Wu

Authors
  1. Ai-Guo Wu
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  2. Guang-Ren Duan
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  3. Yan-Ming Fu
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  4. Wei-Jun Wu
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Correspondence to Ai-Guo Wu.

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Communicated by C.C. Douglas.

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Wu, AG., Duan, GR., Fu, YM. et al. Finite iterative algorithms for the generalized Sylvester-conjugate matrix equation \({AX+BY=E\overline{X}F+S}\) . Computing 89, 147–170 (2010). https://doi.org/10.1007/s00607-010-0100-5

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  • DOI: https://doi.org/10.1007/s00607-010-0100-5

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