Related papers: Generic Regular Decompositions for Generic Zero-Di…

Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

The QCD corrections to the R_{\tau}^{12} moment of the invariant mass distribution in hadronic decays of the tau lepton are discussed. The next-to-next-to-leading order prediction is shown to be stable with respect to change of the…

Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…

Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…

We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…

Software realization of the complex spectra decomposition on unknown number of similarcomponents is proposed.The algorithm is based on non-linear minimizing the sum of squared residuals of the spectrum model. For the adequacy checking the…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

This paper introduces a novel computationally efficient method of solving the 3D single image super-resolution (SR) problem, i.e., reconstruction of a high-resolution volume from its low-resolution counterpart. The main contribution lies in…

Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new…

Regularization techniques help prevent overfitting and therefore improve the ability of convolutional neural networks (CNNs) to generalize. One reason for overfitting is the complex co-adaptations among different parts of the network, which…

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

A presentation of a degree $d$ form in $n+1$ variables as the sum of homogenous elements ``essentially'' involving $n$ variables is called a {\em codimension one decomposition}. Codimension one decompositions are introduced and the related…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty,…

In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain,…