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Verified Error Bounds for Symmetric Solutions of Operator Matrix Equations

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Bio-inspired Computing – Theories and Applications (BIC-TA 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 682))

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Abstract

Based on the interval theory, the verification for symmetric solutions of operator matrix equations \(AX-XB-C=0, A\in \mathbb {R}^{m\times m}, B\in \mathbb {R}^{n\times n}, C\in \mathbb {R}^{m\times n}\) is studied. We propose the algorithm which outputs an approximate symmetric solution and its error bound with the property that an exact solution exists within this computed bound. The proposed algorithm requires only \(O(m^3+n^3)\) operations if A and B are diagonalizable.

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Acknowledgments

This work is supported by Jilin Province Department of Education Science and Technology Research Project under Grants 2014213, 2015131 and 2015156.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Beihua University, Jilin, 132013, Jilin, China

    Qingchun Li, Haifeng Sang & Panpan Liu

  2. College of Economics and Management, Shanghai Maritime University, Shanghai, 201306, China

    Ziyu Li

Authors
  1. Qingchun Li
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  2. Ziyu Li
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  3. Haifeng Sang
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  4. Panpan Liu
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Corresponding author

Correspondence to Haifeng Sang .

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Editors and Affiliations

  1. Xidian University , Xi’an, China

    Maoguo Gong

  2. Huazhong University of Science and Technology, Wuhan, China

    Linqiang Pan

  3. China University of Petroleum, Qingdao, China

    Tao Song

  4. Southwest Jiaotong University , Chengdu, China

    Gexiang Zhang

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© 2016 Springer Nature Singapore Pte Ltd.

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Li, Q., Li, Z., Sang, H., Liu, P. (2016). Verified Error Bounds for Symmetric Solutions of Operator Matrix Equations. In: Gong, M., Pan, L., Song, T., Zhang, G. (eds) Bio-inspired Computing – Theories and Applications. BIC-TA 2016. Communications in Computer and Information Science, vol 682. Springer, Singapore. https://doi.org/10.1007/978-981-10-3614-9_62

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  • DOI: https://doi.org/10.1007/978-981-10-3614-9_62

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3613-2

  • Online ISBN: 978-981-10-3614-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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