Paper Citation Record · LEDGER

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2606.25914.

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pith.paper-citation-record.v1
2606.25914 v1

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measured 31 of 31 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-06-25T19:31:53.096655Z

measured 31 of 31 standing notices

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31 of 31 outbound references displayed

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Outbound references

Observation c64b3186-690b-471a-8c3e-d749cfac2200 · outbound

This paper cites Cambridge Univer- sity Press, 2025.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Cambridge Univer- sity Press, 2025

Reference 1

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Observation 368b2cba-3840-46b2-8355-f1f33bbc7fef · outbound

This paper cites Exact solutions of the boltzmann equation.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Exact solutions of the boltzmann equation

Reference 2

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Observation 5ddf0644-254f-41e3-94e6-e5c43a57d542 · outbound

This paper cites On approximation of the boltzmann equation by discrete velocity models.Comptes rendus de l’Acad´ emie des sciences.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation On approximation of the boltzmann equation by discrete velocity models.Comptes rendus de l’Acad´ emie des sciences

Reference 3

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Observation 57bbc29b-64ba-45ae-817b-4a509f4b4234 · outbound

This paper cites Fast deterministic method of solving the boltzmann equation for hard spheres.European Journal of Mechanics-B/Fluids, 18(5):869–887, 1999.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Fast deterministic method of solving the boltzmann equation for hard spheres.European Journal of Mechanics-B/Fluids, 18(5):869–887, 1999

Reference 4

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Observation 2d63bc60-e6ba-4ede-8b6c-6a29e2640162 · outbound

This paper cites A discrete-velocity scheme for the boltzmann operator of rarefied gas dynamics.Transport Theory and Statistical Physics, 25(1):33–60, 1996.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation A discrete-velocity scheme for the boltzmann operator of rarefied gas dynamics.Transport Theory and Statistical Physics, 25(1):33–60, 1996

Reference 5

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Observation b756435a-87ba-4e7b-a27d-5fe41da00e10 · outbound

This paper cites Interpolatory dynamical low-rank approximation for the 3+ 3d boltzmann–bgk equation.Journal of Computational Physics, page 114515, 2025.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Interpolatory dynamical low-rank approximation for the 3+ 3d boltzmann–bgk equation.Journal of Computational Physics, page 114515, 2025

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation ab5e8f85-341e-42ff-9b8d-e8e9aedff8fb · outbound

This paper cites Parallel cross interpolation for high-precision calculation of high-dimensional integrals.Computer Physics Communications, 246:106869, 2020.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Parallel cross interpolation for high-precision calculation of high-dimensional integrals.Computer Physics Communications, 246:106869, 2020

Reference 7

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Observation ec0a2250-10a6-4c1b-a267-26b32deabdb8 · outbound

This paper cites An efficient dynamical low-rank algorithm for the boltzmann-bgk equation close to the compressible viscous flow regime.SIAM Journal on Scientific Computing, 43(5):B1057–B1080, 2021.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation An efficient dynamical low-rank algorithm for the boltzmann-bgk equation close to the compressible viscous flow regime.SIAM Journal on Scientific Computing, 43(5):B1057–B1080, 2021

Reference 8

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Observation 7acfe60f-2ffe-49b6-9496-ba86444894d9 · outbound

This paper cites Asymptotic-preserving dynamical low-rank method for the stiff nonlinear boltzmann equation.Journal of Computational Physics, 538:114112, 2025.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Asymptotic-preserving dynamical low-rank method for the stiff nonlinear boltzmann equation.Journal of Computational Physics, 538:114112, 2025

Reference 9

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Observation 65d0e9bd-1186-42ba-8f44-2c99db57e3a1 · outbound

This paper cites A re- view of low-rank methods for time-dependent kinetic simulations.Journal of Computational Physics, 538:114191, 2025.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation A re- view of low-rank methods for time-dependent kinetic simulations.Journal of Computational Physics, 538:114191, 2025

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 816569dc-d009-44a8-84a3-45938f005fba · outbound

This paper cites A fast spectral method for the boltzmann collision operator with general collision kernels.SIAM Journal on Scientific Computing, 39(4):B658–B674, 2017.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation A fast spectral method for the boltzmann collision operator with general collision kernels.SIAM Journal on Scientific Computing, 39(4):B658–B674, 2017

Reference 11

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Observation 90e2eecc-4609-47c7-9a05-d315105b62d3 · outbound

This paper cites Galerkin–petrov approach for the boltzmann equation.Journal of Computational Physics, 366:341–365, 2018.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Galerkin–petrov approach for the boltzmann equation.Journal of Computational Physics, 366:341–365, 2018

Reference 12

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Observation ce2f9979-164c-4350-a327-fcaeeed868a7 · outbound

This paper cites Spectral-lagrangian methods for collisional models of non-equilibrium statistical states.Journal of Computational Physics, 228(6):2012–2036, 2009.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Spectral-lagrangian methods for collisional models of non-equilibrium statistical states.Journal of Computational Physics, 228(6):2012–2036, 2009

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 1533c38a-872d-414b-ba70-7980a89c98ce · outbound

This paper cites The Landau equation and Fisher information.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation The Landau equation and Fisher information

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-07-04T20:50:12.134056Z

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Observation abfa4602-ad4f-436f-8c39-8e3e06a178fa · outbound

This paper cites The landau equation does not blow up.Acta Mathematica, 234(2):315– 375, 2025.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation The landau equation does not blow up.Acta Mathematica, 234(2):315– 375, 2025

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 60edaa24-d74d-4da0-8fb5-9117162e1489 · outbound

This paper cites an unresolved cited work.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 4150cea0-9a1c-4a6f-98f2-966b037296bd · outbound

This paper cites An adaptive dynamical low rank method for the nonlinear boltzmann equation.Journal of Scientific Computing, 92(2):75, 2022.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation An adaptive dynamical low rank method for the nonlinear boltzmann equation.Journal of Scientific Computing, 92(2):75, 2022

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 8e892788-bf19-4742-ba71-75aac7cba4ea · outbound

This paper cites The consecutive lifting-projection flow as an approximation of boltzmann and landau flow.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation The consecutive lifting-projection flow as an approximation of boltzmann and landau flow

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 03c679ad-7296-41a8-bef0-66a01389c39d · outbound

This paper cites On the monotonicity of the fisher information for the boltzmann equation.Inventiones mathematicae, 243(1):127–179, 2026.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation On the monotonicity of the fisher information for the boltzmann equation.Inventiones mathematicae, 243(1):127–179, 2026

Reference 19

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Observation 2d74bf8e-b988-4000-b77d-1f1124976fe6 · outbound

This paper cites A polynomial spectral method for the spatially homogeneous boltzmann equation.SIAM Journal on Scientific Computing, 41(1):B27–B49, 2019.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation A polynomial spectral method for the spatially homogeneous boltzmann equation.SIAM Journal on Scientific Computing, 41(1):B27–B49, 2019

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 667fd171-0b62-4364-a2ad-1ebd7fa09abb · outbound

This paper cites Exact solutions of the boltzmann equation.The Physics of Fluids, 20(10):1589–1595, 1977.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Exact solutions of the boltzmann equation.The Physics of Fluids, 20(10):1589–1595, 1977

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 6af8a2a4-fb3c-4d4e-95d8-da877666c8a0 · outbound

This paper cites Quadrature formula for the sphere of 131-th algebraic order of accuracy.Doklady Akademii nauk SSSR, 366(6):741–745, 1999.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Quadrature formula for the sphere of 131-th algebraic order of accuracy.Doklady Akademii nauk SSSR, 366(6):741–745, 1999

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 310f58ef-b2f3-40e0-a8bf-b7c87cf340df · outbound

This paper cites Fast algorithms for computing the boltzmann collision operator.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Fast algorithms for computing the boltzmann collision operator

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 0f92bc75-0f6e-4dfb-a0c7-9d61c9dd0eb0 · outbound

This paper cites an unresolved cited work.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 714137a3-9505-4605-bac6-e6fc897d7cb1 · outbound

This paper cites TT-Toolbox.https://github.com/oseledets/TT-Toolbox, 2026.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation TT-Toolbox.https://github.com/oseledets/TT-Toolbox, 2026

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation e6a96fd3-b470-4a74-b97c-285d6f2e8222 · outbound

This paper cites Tt-cross approximation for multidimensional arrays.Linear Algebra and its Applications, 432(1):70–88, 2010.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Tt-cross approximation for multidimensional arrays.Linear Algebra and its Applications, 432(1):70–88, 2010

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation d695ee9a-441e-4ceb-bebf-38ce93efb513 · outbound

This paper cites Tensor-train decomposition.SIAM Journal on Scientific Computing, 33(5):2295–2317, 2011.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Tensor-train decomposition.SIAM Journal on Scientific Computing, 33(5):2295–2317, 2011

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 85666bf1-f540-441a-a5ff-58aadfe9a26d · outbound

This paper cites Cross approximation in tensor electron density computations.Numerical Linear Algebra with Applications, 17(6):935–952, 2010.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Cross approximation in tensor electron density computations.Numerical Linear Algebra with Applications, 17(6):935–952, 2010

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 857815e8-b25b-421c-8260-7f74599ea146 · outbound

This paper cites Numerical solution of the boltzmann equation i: Spectrally accurate approximation of the collision operator.SIAM journal on numerical analysis, 37(4):1217– 1245, 2000.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Numerical solution of the boltzmann equation i: Spectrally accurate approximation of the collision operator.SIAM journal on numerical analysis, 37(4):1217– 1245, 2000

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-25T19:31:53.096655Z

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Observation 63bf9814-95b9-47c8-b2a5-08d0e65039ba · outbound

This paper cites Savostyanov.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Savostyanov

Reference 30

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Observation bba9f2d3-743c-459e-a6cf-bd04a399a292 · outbound

This paper cites Approximation of the boltzmann collision operator based on hermite spectral method.Journal of Computational Physics, 397:108815, 2019.

A fast scheme for the homogeneous Boltzmann equation based on lifting and tensor train approximation Approximation of the boltzmann collision operator based on hermite spectral method.Journal of Computational Physics, 397:108815, 2019

Reference 31

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