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Title: Collocation methods for nonlinear differential equations on low-rank manifolds

Journal Article · · Linear Algebra and Its Applications

Not Available

Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
2476403
Journal Information:
Linear Algebra and Its Applications, Journal Name: Linear Algebra and Its Applications Journal Issue: C Vol. 705; ISSN 0024-3795
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (41)

Distributed hierarchical SVD in the Hierarchical Tucker format journal March 2018
On manifolds of tensors of fixed TT-rank journal September 2011
A projector-splitting integrator for dynamical low-rank approximation journal November 2013
An unconventional robust integrator for dynamical low-rank approximation journal May 2021
A rank-adaptive robust integrator for dynamical low-rank approximation journal January 2022
Implicit Integration of Nonlinear Evolution Equations on Tensor Manifolds journal September 2023
Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential Equations journal August 2024
Coordinate-Adaptive Integration of PDEs on Tensor Manifolds journal February 2024
Ground state structures in ordered binary alloys with second neighbor interactions journal March 1972
Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases journal February 2023
A DEIM Tucker tensor cross algorithm and its application to dynamical low-rank approximation journal April 2024
Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds journal December 2024
Parallel cross interpolation for high-precision calculation of high-dimensional integrals journal January 2020
A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems journal September 2017
Unnormalized optimal transport journal December 2019
Dynamic tensor approximation of high-dimensional nonlinear PDEs journal July 2021
A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps journal June 2022
A robust and conservative dynamical low-rank algorithm journal July 2023
Tensor rank reduction via coordinate flows journal October 2023
TT-cross approximation for multidimensional arrays journal January 2010
The geometry of algorithms using hierarchical tensors journal July 2013
Quasioptimality of maximum-volume cross interpolation of tensors journal October 2014
Dynamically orthogonal field equations for continuous stochastic dynamical systems journal December 2009
The numerical approximation of nonlinear functionals and functional differential equations journal February 2018
Quantized tensor networks for solving the Vlasov–Maxwell equations journal June 2024
Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics journal January 2015
Tensor approximation of functional differential equations journal July 2024
Tensor Decompositions and Applications journal August 2009
Tensor-Train Decomposition journal January 2011
Hierarchical Singular Value Decomposition of Tensors journal January 2010
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors journal January 2013
Time Integration of Tensor Trains journal January 2015
A DEIM Induced CUR Factorization journal January 2016
A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation journal January 2018
Stability of Discrete Empirical Interpolation and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic Sampling Points journal January 2020
Time Integration of Tree Tensor Networks journal January 2021
Functional Tucker Approximation Using Chebyshev Interpolation journal January 2021
Randomized Algorithms for Rounding in the Tensor-Train Format journal January 2023
A Conservative Low Rank Tensor Method for the Vlasov Dynamics journal January 2024
Energy Stable and Conservative Dynamical Low-Rank Approximation for the Su–Olson Problem journal April 2024
Fourth-Order Time-Stepping for Stiff PDEs journal January 2005