An S-type singular value inclusion set for rectangular tensors
نویسنده
چکیده
An S-type singular value inclusion set for rectangular tensors is given. Based on the set, new upper and lower bounds for the largest singular value of nonnegative rectangular tensors are obtained and proved to be sharper than some existing results. Numerical examples are given to verify the theoretical results.
منابع مشابه
A new S-type upper bound for the largest singular value of nonnegative rectangular tensors
By breaking [Formula: see text] into disjoint subsets S and its complement, a new S-type upper bound for the largest singular value of nonnegative rectangular tensors is given and proved to be better than some existing ones. Numerical examples are given to verify the theoretical results.
متن کاملOn Generic Nonexistence of the Schmidt-Eckart-Young Decomposition for Complex Tensors
The Schmidt-Eckart-Young theorem for matrices states that the optimal rank-r approximation to a matrix is obtained by retaining the first r terms from the singular value decomposition of that matrix. This work considers a generalization of this optimal truncation property to the CANDECOMP/PARAFAC decomposition of tensors and establishes a necessary orthogonality condition. We prove that this co...
متن کاملBest subspace tensor approximations
In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained via the singular value decomposition which allows to compute the best rank k approximations. For t-tensors with t > 2 many generalizations of the singular val...
متن کاملOn the interconnection between the higher-order singular values of real tensors
A higher-order tensor allows several possible matricizations (reshapes into matrices). The simultaneous decay of singular values of such matricizations has crucial implications on the low-rank approximability of the tensor via higher-order singular value decomposition. It is therefore an interesting question which simultaneous properties the singular values of different tensor matricizations ac...
متن کاملA Third-order Generalization of the Matrix Svd as a Product of Third-order Tensors
Abstract. Traditionally, extending the Singular Value Decomposition (SVD) to third-order tensors (multiway arrays) has involved a representation using the outer product of vectors. These outer products can be written in terms of the n-mode product, which can also be used to describe a type of multiplication between two tensors. In this paper, we present a different type of third-order generaliz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره 2017 شماره
صفحات -
تاریخ انتشار 2017