相关论文: Frontal Slice Approaches for Tensor Linear Systems

Randomized iterative algorithms, such as the randomized Kaczmarz method and the randomized Gauss-Seidel method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our…

We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…

Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

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…

It is well-known that a multilinear system with a nonsingular M-tensor and a positive right-hand side has a unique positive solution. Tensor splitting methods generalizing the classical iterative methods for linear systems have been…

This paper describes solution methods for linear discrete ill-posed problems defined by third order tensors and the t-product formalism introduced in [M. E. Kilmer and C. D. Martin, Factorization strategies for third order tensors, Linear…

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods…

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor…

A adapted tensor-structured GMRES method for the TT format is proposed and investigated. The Tensor Train (TT) approximation is a robust approach to high-dimensional problems. One class of problems is solution of a linear system. In this…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…