Paper Citation Record · LEDGER

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids

As of 16 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2412.14460.

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2412.14460 v2

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Observation e8054fe9-212f-4182-bfbf-7d72adca6fa7 · outbound

This paper cites Quarteroni, A.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Quarteroni, A

Reference 1

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Observation e2749180-adb6-467c-90b9-fe9490ba87a3 · outbound

This paper cites Reduced basis approx imation of parametrized optimal ﬂow control problems for the Stokes equations.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Reduced basis approx imation of parametrized optimal ﬂow control problems for the Stokes equations

Reference 2

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This paper cites Reduced basis approx imation and a posteriori error estimation for Stokes ﬂows in parametrized geometries: roles of the inf–sup stabi lity constants.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Reduced basis approx imation and a posteriori error estimation for Stokes ﬂows in parametrized geometries: roles of the inf–sup stabi lity constants

Reference 3

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This paper cites An algebraic least squares reduced basis method for the solution of nonafﬁnely parametrized Stokes equations.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids An algebraic least squares reduced basis method for the solution of nonafﬁnely parametrized Stokes equations

Reference 4

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This paper cites Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

Reference 5

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Observation a912626d-1b46-4df0-8897-e8edad690e4c · outbound

This paper cites Space-Time Re duced Basis Methods for Parametrized Unsteady Stokes Equations.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Space-Time Re duced Basis Methods for Parametrized Unsteady Stokes Equations

Reference 6

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Observation 056e221a-4937-402d-b104-e61c5742e2ac · outbound

This paper cites Model order reduction with nove l discrete empirical interpolation methods in space–time.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Model order reduction with nove l discrete empirical interpolation methods in space–time

Reference 7

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Observation fa88bf88-05e1-49d5-8a85-faa943b34d59 · outbound

This paper cites Reliable Real-Time Solution of Par ametrized Partial Differential Equations: Reduced-Basis Output Bound Methods.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Reliable Real-Time Solution of Par ametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

Reference 8

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Observation e69837f3-478c-48be-abbb-a1ee5609e098 · outbound

This paper cites A Mathe matical and Computational Framework for Reli- able Real-Time Solution of Parametrized Partial Different ial Equations.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids A Mathe matical and Computational Framework for Reli- able Real-Time Solution of Parametrized Partial Different ial Equations

Reference 9

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Observation 15b46f3a-68ed-4d23-a6e9-9b7cff3a401b · outbound

This paper cites Numerical tensor calculus.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Numerical tensor calculus

Reference 10

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This paper cites Hackbusch.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Hackbusch

Reference 11

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This paper cites Some mathematical notes on three-mode fa ctor analysis.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Some mathematical notes on three-mode fa ctor analysis

Reference 12

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This paper cites TT-cross approxima tion for multidimensional arrays.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids TT-cross approxima tion for multidimensional arrays

Reference 13

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Observation b981e15a-d1f3-4fc4-806a-f948eb56525b · outbound

This paper cites Tensor-train decomposition.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Tensor-train decomposition

Reference 14

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Observation ad743aeb-4750-47ea-a627-451365a955c7 · outbound

This paper cites A continu ous analogue of the tensor-train decomposition.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids A continu ous analogue of the tensor-train decomposition

Reference 15

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Observation dc004072-3983-49ba-8c3d-15898700c0a4 · outbound

This paper cites Spect ral tensor-train decomposition.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Spect ral tensor-train decomposition

Reference 16

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Observation 70012529-72b1-4ff8-ae67-d972ce14ff24 · outbound

This paper cites Deep composition of Tensor-Train s using squared inverse Rosenblatt transports.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Deep composition of Tensor-Train s using squared inverse Rosenblatt transports

Reference 17

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Observation 53f03767-f3cf-4e3e-952e-e0365f7636e8 · outbound

This paper cites Approximation and sampling of multivariate probability distributions in the tensor train decomposition.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Approximation and sampling of multivariate probability distributions in the tensor train decomposition

Reference 18

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This paper cites Alternating minima l energy methods for linear systems in higher dimensions.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Alternating minima l energy methods for linear systems in higher dimensions

Reference 19

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This paper cites Pseudo-skeleton approximations by matrices of maximal volume.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Pseudo-skeleton approximations by matrices of maximal volume

Reference 20

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This paper cites A priori analysis of a tensor ROM for parameter dependent parabolic problems.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids A priori analysis of a tensor ROM for parameter dependent parabolic problems

Reference 21

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This paper cites Interpolatory tens orial reduced order models for parametric dynamical sys- tems.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Interpolatory tens orial reduced order models for parametric dynamical sys- tems

Reference 22

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This paper cites The aggregated unﬁtted ﬁnite element method for elliptic problems.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids The aggregated unﬁtted ﬁnite element method for elliptic problems

Reference 23

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This paper cites Kolmogorov n-widths for line ar dynamical systems.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Kolmogorov n-widths for line ar dynamical systems

Reference 24

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This paper cites Collocation methods for nonlinear differential equations on low-rank manifolds.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Collocation methods for nonlinear differential equations on low-rank manifolds

Reference 25

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This paper cites Nitsche’s method for interface problems in computational mechanics.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Nitsche’s method for interface problems in computational mechanics

Reference 26

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This paper cites Fictitious domain methods usi ng cut elements: III. A stabilized Nitsche method for Stokes’ problem.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Fictitious domain methods usi ng cut elements: III. A stabilized Nitsche method for Stokes’ problem

Reference 27

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This paper cites The Finite Element Method in D imension Two.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids The Finite Element Method in D imension Two

Reference 28

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This paper cites Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

Reference 29

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A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Ho et al

Reference 30

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A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Gaussian Elimination and Its V ariants

Reference 31

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This paper cites Galerkin v. least –squares Petrov–Galerkin projection in nonlinear model reduction.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Galerkin v. least –squares Petrov–Galerkin projection in nonlinear model reduction

Reference 32

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This paper cites S upremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equa tions.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids S upremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equa tions

Reference 33

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This paper cites The Alternat ing Linear Scheme for Tensor Optimization in the Tensor Train Format.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids The Alternat ing Linear Scheme for Tensor Optimization in the Tensor Train Format

Reference 34

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A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Solution of Linear Sys tems and Matrix Inversion in the TT-Format

Reference 35

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A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Nonlinear model r eduction via discrete empirical interpolation

Reference 36

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This paper cites Efﬁcient model r eduction of parametrized systems by matrix discrete em- pirical interpolation.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Efﬁcient model r eduction of parametrized systems by matrix discrete em- pirical interpolation

Reference 37

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This paper cites 07 - Sampling and R econstruction.

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids 07 - Sampling and R econstruction

Reference 38

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A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Mueller and S

Reference 39

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A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids Unresolved cited work

Reference 2025

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