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Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…

The Golub-Kahan-Tikhonov method is a popular solution technique for large linear discrete ill-posed problems. This method first applies partial Golub-Kahan bidiagonalization to reduce the size of the given problem and then uses Tikhonov…

This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental…

The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…

In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…

This paper derives the CS decomposition for orthogonal tensors (T-CSD) and the generalized singular value decomposition for two tensors (T-GSVD) via the T-product. The structures of the two decompositions are analyzed in detail and are…

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 paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space-dimensions. The matrix…

GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as Dirichlet boundary value problems for elliptic partial…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

We consider linear ill-conditioned operator equations in a Hilbert space setting. Motivated by the aggregation method, we consider approximate solutions constructed from linear combinations of Tikhonov regularization, which amounts to…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…

For the solution of linear discrete ill-posed problems, in this paper we consider the Arnoldi-Tikhonov method coupled with the Generalized Cross Validation for the computation of the regularization parameter at each iteration. We study the…

We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

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 are interested in developing iterative Krylov subspace methods in tensor structure to solve a class of multilinear systems via Einstein product. In particular, we develop global variants of the GMRES and…