Publication

Algorithm 941: htucker-A MATLAB Toolbox for Tensors in Hierarchical Tucker Format

Daniel Kressner, Christine Tobler
2014
Journal Articles

Abstract

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a MATLAB toolbox, along with the underlying methodology and algorithms, which provides a convenient way to work with this format. The toolbox not only allows for the efficient storage and manipulation of tensors in hierarchical Tucker format but also offers a set of tools for the development of higher-level algorithms. Several examples for the use of the toolbox are given.

Official source

https://infoscience.epfl.ch/entities/publication/ee7aeffa-6227-4d14-8c36-1625a5c384ab

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Daniel Kressner, Christine Tobler
2014
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ee7aeffa-6227-4d14-8c36-1625a5c384ab

About this result

Related concepts (31)

Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product.

Symmetric tensor

In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: for every permutation σ of the symbols {1, 2, ..., r}. Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies The space of symmetric tensors of order r on a finite-dimensional vector space V is naturally isomorphic to the dual of the space of homogeneous polynomials of degree r on V.

Tensor (intrinsic definition)

In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. In differential geometry an intrinsic geometric statement may be described by a tensor field on a manifold, and then doesn't need to make reference to coordinates at all.

Related publications (30)

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Robert Dalang, Fei Pu

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

Springer/Plenum Publishers2024

Reliable data-driven decision-making through optimal transport

Bahar Taskesen

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

EPFL2024

Dynamical system approach to navigation around obstacles

Aude Billard, Aradhana Nayak

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

2024