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Successive Partial-Symmetric Rank-One Algorithms for Almost Unitarily Decomposable Conjugate Partial-Symmetric Tensors

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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.

Keywords

Approximation algorithm Complex tensor Perturbation analysis 

Mathematics Subject Classification

15A69 49M27 53A45 68W25 

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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina
  2. 2.School of Mathematical Sciences, and MOE-LSCShanghai Jiao Tong UniversityShanghaiChina

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