相关论文: Shifted Power Method for Computing Tensor Eigenpai…

In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly…

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in parallel. In order to…

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and…

We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…

This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…

In this work, we present a new characterization of symmetric $H^+$-tensors. It is known that a symmetric tensor is an $H^+$-tensor if and only if it is a generalized diagonally dominant tensor with nonnegative diagonal elements. By…

In this paper, we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition. We establish the weak convergence, global convergence…

In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…

The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…

We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…

Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace…

We present a new power method to obtain solutions of eigenvalue problems. The method can determine not only the dominant or lowest eigenvalues but also all eigenvalues without the need for a deflation procedure. The method uses a functional…

In this paper, we mainly develop the well-known vector and matrix polynomial extrapolation methods in tensor framework. To this end, some new products between tensors are defined and the concept of positive definitiveness is extended for…

The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor $\mathcal{X}$ as a product of a core tensor $\mathcal{S}$, a matrix $C$ obtained by…

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…

We consider tensor data completion of an incomplete observation of multidimensional harmonic (MH) signals. Unlike existing tensor-based techniques for MH retrieval (MHR), which mostly adopt the canonical polyadic decomposition (CPD) to…

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…