Abstract
In this paper, we introduce the almost unitarily decomposable conjugate partial-symmetric tensors, which are different from the commonly studied orthogonally decomposable tensors by involving the conjugate terms in the decomposition and the perturbation term. We not only show that successive rank-one approximation algorithm exactly recovers the unitary decomposition of the unitarily decomposable conjugate partial-symmetric tensors. The perturbation analysis of successive rank-one approximation algorithm for almost unitarily decomposable conjugate partial-symmetric tensors is also provided to demonstrate the robustness of the algorithm.
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This paper is dedicated to Professor Yin-Yu Ye in celebration of his 70th birthday.
This work was partially supported by the National Natural Science Foundation of China (No. 11571234).
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Fu, TR., Fan, JY. Successive Partial-Symmetric Rank-One Algorithms for Almost Unitarily Decomposable Conjugate Partial-Symmetric Tensors. J. Oper. Res. Soc. China 7, 147–167 (2019). https://doi.org/10.1007/s40305-018-0194-6
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DOI: https://doi.org/10.1007/s40305-018-0194-6