Related papers: Generalized L-product for hight order tensors with…
We derive integral formulas that simplify the Vector Spherical Tensor Product recently introduced by Xie et al., which generalizes the Gaunt tensor product to antisymmetric couplings. In particular, we obtain explicit closed-form…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
The tensor t-product, introduced by Kilmer and Martin [26], is a powerful tool for the analysis of and computation with third-order tensors. This paper introduces eigentubes and eigenslices of third-order tensors under the t-product. The…
In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
We define a general product of two $n$-dimensional tensors $\mathbb {A}$ and $\mathbb {B}$ with orders $m\ge 2$ and $k\ge 1$, respectively. This product is a generalization of the usual matrix product, and satisfies the associative law.…
This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based…
In this paper, we present the definition of generalized tensor function according to the tensor singular value decomposition (T-SVD) via the tensor T-product. Also, we introduce the compact singular value decomposition (T-CSVD) of tensors…
Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…
We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
In the present paper, we introduce new tensor Krylov subspace methods for solving linear tensor equations. The proposed methods use the well known T-product for tensors and tensor subspaces related to tube fibers. We introduce some new…
In the present paper, we introduce new tensor krylov subspace methods for solving large Sylvester tensor equations. The proposed method uses the well-known T-product for tensors and tensor subspaces. We introduce some new tensor products…
In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and…
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…
Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…