Related papers: A Lanczos-type procedure for tensors
We provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of the problem is of general reaction-convection-diffusion type.…
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre…
Quadratic forms of Hermitian matrix resolvents involve the solutions of shifted linear systems. Efficient iterative solutions use the shift-invariance property of Krylov subspaces The Hermitian Lanczos method reduces a given vector and…
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented…
Based on the tensor-based large margin distribution and the nonparallel support tensor machine, we establish a novel classifier for binary classification problem in this paper, termed the Large Margin Distribution based NonParallel Support…
The aim of this paper is twofold. First, we obtain the explicit exact formal solutions of differential equations of different types in the form with Dyson chronological operator exponents. This allows us to deal directly with the solutions…
We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar…
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…
In this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs (MIMO). This approach is based on the projection of the initial problem onto…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…
We contribute to the method of trigonometric series for solving differential equations of certain non linear oscillators. Key Words: series power solution, trigonometric series.
We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…
Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…
We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these…
We develop an efficient, unconditionally stable, variable step second order exponential time differencing scheme for the incompressible Navier Stokes equations in two and three spatial dimensions under periodic boundary conditions, together…
This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light (and with the jargon) of theory of topological insulators. In particular it is shown that the Landau…