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Numerical solutions of AXB = C for mirrorsymmetric matrix X under a specified submatrix constraint

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Abstract

Mirrorsymmetric matrices, which are the iteraction matrices of mirrorsymmetric structures, have important application in studying odd/even-mode decomposition of symmetric multiconductor transmission lines (MTL). In this paper we present an efficient algorithm for minimizing \({\|AXB-C\|}\) where \({\|\cdot\|}\) is the Frobenius norm, \({A\in \mathbb{R}^{m\times n}}\), \({B\in \mathbb{R}^{n\times s}}\), \({C\in \mathbb{R}^{m\times s}}\) and \({X\in \mathbb{R}^{n\times n}}\) is mirrorsymmetric with a specified central submatrix [x ij ]r≤i, j≤n-r. Our algorithm produces a suitable X such that AXB = C in finitely many steps, if such an X exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Jiao-Fen Li & Xue-Feng Duan

  2. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Xi-Yan Hu & Lei Zhang

Authors
  1. Jiao-Fen Li
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  2. Xi-Yan Hu
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  3. Xue-Feng Duan
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  4. Lei Zhang
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Corresponding author

Correspondence to Jiao-Fen Li.

Additional information

Communicated by C.C. Douglas.

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Li, JF., Hu, XY., Duan, XF. et al. Numerical solutions of AXB = C for mirrorsymmetric matrix X under a specified submatrix constraint. Computing 90, 39–56 (2010). https://doi.org/10.1007/s00607-010-0109-9

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  • DOI: https://doi.org/10.1007/s00607-010-0109-9

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Mathematics Subject Classification (2000)