A Constructive Algorithm for Decomposing a Tensor into a Finite Sum of Orthonormal Rank-1 Terms
نویسندگان
چکیده
Abstract. We propose a novel and constructive algorithm that decomposes an arbitrary tensor into a finite sum of orthonormal rank-1 outer factors. The algorithm, named TTr1SVD, works by converting the tensor into a rank-1 tensor train (TT) series via singular value decomposition (SVD). TTr1SVD naturally generalizes the SVD to the tensor regime and delivers elegant notions of tensor rank and error bounds, and readily quantifies a low-rank approximation to the original tensor.
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عنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 36 شماره
صفحات -
تاریخ انتشار 2015