research-article

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

Authors:

Daniel Kressner,

Christine ToblerAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 40, Issue 3

Article No.: 22, Pages 1 - 22

https://doi.org/10.1145/2538688

Published: 01 April 2014 Publication History

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.

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Cited By

Rodgers AVenturi D(2024)Tensor approximation of functional differential equationsPhysical Review E10.1103/PhysRevE.110.015310110:1Online publication date: 30-Jul-2024
https://doi.org/10.1103/PhysRevE.110.015310
Sulz DLubich CCeruti GLesanovsky ICarollo F(2024)Numerical simulation of long-range open quantum many-body dynamics with tree tensor networksPhysical Review A10.1103/PhysRevA.109.022420109:2Online publication date: 13-Feb-2024
https://doi.org/10.1103/PhysRevA.109.022420
Sutti MVandereycken B(2024)Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential EquationsJournal of Scientific Computing10.1007/s10915-024-02629-8101:1Online publication date: 13-Aug-2024
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Index Terms

Algorithm 941: htucker---A Matlab Toolbox for Tensors in Hierarchical Tucker Format
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
  2. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 40, Issue 3

April 2014

152 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2610268

Editor:
Michael A. Heroux
Sandia National Laboratories USA

Issue’s Table of Contents

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 April 2014

Accepted: 01 October 2013

Revised: 01 September 2013

Received: 01 February 2012

Published in TOMS Volume 40, Issue 3

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Cited By

Rodgers AVenturi D(2024)Tensor approximation of functional differential equationsPhysical Review E10.1103/PhysRevE.110.015310110:1Online publication date: 30-Jul-2024
https://doi.org/10.1103/PhysRevE.110.015310
Sulz DLubich CCeruti GLesanovsky ICarollo F(2024)Numerical simulation of long-range open quantum many-body dynamics with tree tensor networksPhysical Review A10.1103/PhysRevA.109.022420109:2Online publication date: 13-Feb-2024
https://doi.org/10.1103/PhysRevA.109.022420
Sutti MVandereycken B(2024)Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential EquationsJournal of Scientific Computing10.1007/s10915-024-02629-8101:1Online publication date: 13-Aug-2024
https://dl.acm.org/doi/10.1007/s10915-024-02629-8
Benner PRichter TWeinhandl R(2024)A low‐rank method for parameter‐dependent fluid‐structure interaction discretizations with hyperelasticityZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik10.1002/zamm.202300562104:10Online publication date: 24-Aug-2024
https://doi.org/10.1002/zamm.202300562
Ceruti GLubich CSulz D(2023)Rank-Adaptive Time Integration of Tree Tensor NetworksSIAM Journal on Numerical Analysis10.1137/22M147379061:1(194-222)Online publication date: 23-Feb-2023
https://doi.org/10.1137/22M1473790
Masetti GRobol LChiaradonna SGiandomenico F(2023)Implicit Reward Structures for Implicit Reliability ModelsIEEE Transactions on Reliability10.1109/TR.2022.319091572:2(774-794)Online publication date: Jun-2023
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Kallullathil SCarrington. T(2023)Computing vibrational energy levels using a canonical polyadic tensor method with a fixed rank and a contraction treeThe Journal of Chemical Physics10.1063/5.0149832158:21Online publication date: 1-Jun-2023
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Rodgers AVenturi D(2023)Implicit Integration of Nonlinear Evolution Equations on Tensor ManifoldsJournal of Scientific Computing10.1007/s10915-023-02352-w97:2Online publication date: 23-Sep-2023
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Allmann-Rahn FGrauer RKormann K(2022)A parallel low-rank solver for the six-dimensional Vlasov–Maxwell equationsJournal of Computational Physics10.1016/j.jcp.2022.111562469:COnline publication date: 15-Nov-2022
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Guo WQiu J(2022)A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow mapsJournal of Computational Physics10.1016/j.jcp.2022.111089458:COnline publication date: 1-Jun-2022
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