Related papers: Tensor product approximations of high dimensional …
We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain $[a,b]^2=[a,b]\times [a,b]$. Our modified cubature formulae use mixed type data: except evaluations of the…
This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…
Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…
We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld "coproduct". This allow us to recover the vector representations recently introduced by Feigin-Jimbo-Miwa-Mukhin [6] and…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of…
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is…
We propose, analyze, and implement interpolatory approximations and Filon-type cubature for efficient and accurate evaluation of a class of wideband generalized Fourier integrals on the sphere. The analysis includes derivation of (i)…