Spectral norm and nuclear norm of a third order tensor

نویسندگان

چکیده

<p style="text-indent:20px;">The spectral norm and the nuclear of a third order tensor play an important role in completion recovery problem. We show that is equal to square root three positive semi-definite biquadratic tensors, roots norms those tensors are lower bounds tensor. This provides way estimate evaluate Some upper for tensor, by radii some symmetric matrices, presented.</p>

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computational Complexity of Tensor Nuclear Norm

The main result of this paper is that the weak membership problem in the unit ball of a given norm is NP-hard if and only if the weak membership problem in the unit ball of the dual norm is NP-hard. Equivalently, the approximation of a given norm is polynomial time if and only if the approximation of the dual norm is polynomial time. Using the NP-hardness of the approximation of spectral norm o...

متن کامل

On Tensor Completion via Nuclear Norm Minimization

Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To overcome these difficulties, existing approaches often proceed by unfolding tensors into matrices and then apply techniques for matrix completion. We show here th...

متن کامل

Nuclear norm of higher-order tensors

We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field — the value of the nuclear norm of a real 3-tensor depends on whether we regard it as a real 3-tensor or a complex 3-tensor with real entries. We show that every tensor has a nuclear norm attainin...

متن کامل

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

15 صفحه اول

A Weighted Nuclear Norm Method for Tensor Completion

In recent years, tensor completion problem has received a significant amount of attention in computer vision, data mining and neuroscience. It is the higher order generalization of matrix completion. And these can be solved by the convex relaxation which minimizes the tensor nuclear norm instead of the n-rank of the tensor. In this paper, we introduce the weighted nuclear norm for tensor and de...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Industrial and Management Optimization

سال: 2022

ISSN: ['1547-5816', '1553-166X']

DOI: https://doi.org/10.3934/jimo.2021010