相关论文: A DEIM Tucker Tensor Cross Algorithm and its Appli…

This paper proposes two new algorithms related to the Tucker tensor format. The first method is a new cross approximation for Tucker tensors, which we call Cross$^2$-DEIM. Cross$^2$-DEIM is an iterative method that uses a fiber sampling…

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM…

This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…

The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field, the geometric inner-product structure suffices to introduce…

We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network…

The discrete empirical interpolation method (DEIM) is a well-established approach, widely used for state reconstruction using sparse sensor/measurement data, nonlinear model reduction, and interpretable feature selection. We introduce the…

The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…

In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it…

Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time-dependent partial differential equations on tensorized…

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…

An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

In general, matrix or tensor-valued functions are approximated using the method developed for vector-valued functions by transforming the matrix-valued function into vector form. This paper proposes a tensor-based interpolation method to…

We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…

The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…

Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…