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The solution of fuzzy Sylvester matrix equation

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Abstract

In this paper, A fuzzy Sylvester matrix equation with crisp coefficient matrices is considered. We use the arithmetic operation rule of fuzzy number to transfer the equation into two crisp Sylvester matrix equations, which avoids using Kronecker operation and which makes it possible to apply some existing methods to solve Sylvester matrix equation. Since the two transferred equations keep the number of unknowns unchanged, numerical operations needed in our method are much less than the operations in the method using Kronecker product. At last, we use several small-scale examples to illustrate the correctness of our method and several large-scale examples to illustrate the efficiency of our method.

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Acknowledgements

This study was funded by National Natural Science Foundation of China under Grant NSF11271081.

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Authors and Affiliations

  1. Mathematical School Zhejiang College, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Qixiang He

  2. Mathematics School, The Laboratory of Computational Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Liangshao Hou

  3. Mathematics School, Shanghai Key Laboratory of Financial Information Technology, The Laboratory of Computational Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Jieyong Zhou

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  1. Qixiang He
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  2. Liangshao Hou
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  3. Jieyong Zhou
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Correspondence to Jieyong Zhou.

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Communicated by V. Loia.

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He, Q., Hou, L. & Zhou, J. The solution of fuzzy Sylvester matrix equation. Soft Comput 22, 6515–6523 (2018). https://doi.org/10.1007/s00500-017-2702-8

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  • DOI: https://doi.org/10.1007/s00500-017-2702-8

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