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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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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