Related papers: Spectral Methods for Matrices and Tensors

This is a survey about spectral sets, to appear in the second edition of Handbook of Linear Algebra (L. Hogben, ed.). Spectral sets and K-spectral sets, introduced by John von Neumann, offer a possibility to estimate the norm of functions…

For tensor linear systems with respect to the popular t-product, we first present the sketch-and-project method and its adaptive variants. Their Fourier domain versions are also investigated. Then, considering that the existing sketching…

In this article we consider min-min type of problems or minimization by two groups of variables. Min-min problems may occur in case if some groups of variables in convex optimization have different dimensions or if these groups have…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

The paper presents an analysis of the possible spectra manipulation and its consequence for the specific application of XCT. The focus was on the modification of the registered spectra dominantly by the sewing/stitching method. A model…

Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…

A new method of matrix spectral factorization is proposed which reliably computes an approximate spectral factor of any matrix spectral density that admits spectral factorization

Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

Recurrent neural networks (RNNs) are a class of neural networks used in sequential tasks. However, in general, RNNs have a large number of parameters and involve enormous computational costs by repeating the recurrent structures in many…

This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem.…