Paper Citation Record · LEDGER

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems

As of 4 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2606.25643.

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pith.paper-citation-record.v1
2606.25643 v1

Coverage vector

measured 32 of 32 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-06-25T20:47:08.643597Z

measured 32 of 32 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

32 of 32 outbound references displayed

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External citation measurements

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Outbound references

Observation e5441b08-71e5-4dd7-a2c3-c63ac792947a · outbound

This paper cites Solovchuk, Tony W.

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Solovchuk, Tony W

Reference 1

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Observation 4f681ee3-cb85-46ce-8d3b-89873bf55a10 · outbound

This paper cites Nonlinear resonant phenomena in multilevel quantum systems[D].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Nonlinear resonant phenomena in multilevel quantum systems[D]

Reference 2

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Observation 12324ff8-f4a6-4834-84bf-68836aeb39b7 · outbound

This paper cites Fast image inpainting based on coherence trans- port[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Fast image inpainting based on coherence trans- port[J]

Reference 3

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Observation a264d5f9-87b5-4d6b-9e0a-eb7a9ec30e74 · outbound

This paper cites Advances in the mechanics of undamageable materials: General three-dimensional formulation[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Advances in the mechanics of undamageable materials: General three-dimensional formulation[J]

Reference 4

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Observation 1201ce6c-2de9-457a-8606-a13bfea70bed · outbound

This paper cites High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-level stability and transition[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-level stability and transition[J]

Reference 5

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Observation bbc4d9f5-b3b0-4039-9c34-146c992ba987 · outbound

This paper cites JAX-Fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems JAX-Fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows[J]

Reference 6

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Observation 0c3ce707-895b-4960-8eb9-884c798cf835 · outbound

This paper cites Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics[J]

Reference 7

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Observation 669f2379-19b1-4f44-9f4b-6eb55eb327b8 · outbound

This paper cites Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation ddfcea5f-f005-4f71-8ed4-590eefebe9d2 · outbound

This paper cites Existence and Computation of Low Kronecker-Rank Approxima- tions for Large Linear Systems of Tensor Product Structure[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Existence and Computation of Low Kronecker-Rank Approxima- tions for Large Linear Systems of Tensor Product Structure[J]

Reference 9

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Observation 0a2a4081-b328-45bf-acfa-7d51577ea258 · outbound

This paper cites Chebyshev collocation spectral methods for coupled radiation and conduction in a concentric spherical participating medium(Article)[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Chebyshev collocation spectral methods for coupled radiation and conduction in a concentric spherical participating medium(Article)[J]

Reference 10

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Observation e14e2e39-efdc-48cc-9134-875ef5750ae7 · outbound

This paper cites A projection method and Kronecker product preconditioner for solving Sylvester tensor equations[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A projection method and Kronecker product preconditioner for solving Sylvester tensor equations[J]

Reference 11

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Observation fe950a27-369d-4ae8-84f8-72ac887fe0c2 · outbound

This paper cites On the solution to the Sylvester matrix equationAV+BW= EV F[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems On the solution to the Sylvester matrix equationAV+BW= EV F[J]

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 5144e66d-ef13-41da-bd79-f59f68739df4 · outbound

This paper cites A complete analytical solution to the equationT A−F T=LCand its applications[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A complete analytical solution to the equationT A−F T=LCand its applications[J]

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation d8ddf9be-d499-483f-9422-4eb34e6a4306 · outbound

This paper cites Pole assignment for linear and quadratic systems with Time-delay in control[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Pole assignment for linear and quadratic systems with Time-delay in control[J]

Reference 14

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Observation 6f33ec67-6ad0-4719-a347-0b5335257d58 · outbound

This paper cites Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method[J]

Reference 15

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Observation fabae6c1-3a5e-4239-adca-d79958c125e2 · outbound

This paper cites On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations[J]

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 28c0b00d-b81f-4178-8f86-a1b4a48efd7e · outbound

This paper cites On global iterative schemes based on Hessenberg process for (ill-posed) Sylvester tensor equations[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems On global iterative schemes based on Hessenberg process for (ill-posed) Sylvester tensor equations[J]

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation ee1963c7-32b2-4d5c-b5c6-5943d9f8e926 · outbound

This paper cites A tensor format for the general- ized Hessenberg method for solving Sylvester tensor equations[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A tensor format for the general- ized Hessenberg method for solving Sylvester tensor equations[J]

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 153ff994-d9a0-4ce0-8e90-1c4bbfcd4d5f · outbound

This paper cites Researches on the iterative algorithms for several classes of matrix equations and tensor equations[D].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Researches on the iterative algorithms for several classes of matrix equations and tensor equations[D]

Reference 19

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Observation a0610ff2-8072-4134-b434-fb7833ab68cb · outbound

This paper cites A Tensor multigrid method for solving Sylvester tensor equations[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A Tensor multigrid method for solving Sylvester tensor equations[J]

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 9a4d8151-e492-413b-9f40-a9f03acfd433 · outbound

This paper cites The cascadic multigrid method for elliptic prob- lems[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems The cascadic multigrid method for elliptic prob- lems[J]

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 6f67c05c-1c18-44e2-a634-5ba0c1a7ef1c · outbound

This paper cites A new class of cascadic multigrid method, Sci.

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A new class of cascadic multigrid method, Sci

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation baa0fc69-6964-421c-8d6f-bff6d943deff · outbound

This paper cites an unresolved cited work.

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation ad8524d2-53ea-4da6-80d5-be391adbda1f · outbound

This paper cites A modulus-based cascadic multigrid method for elliptic vari- ational inequality problems[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A modulus-based cascadic multigrid method for elliptic vari- ational inequality problems[J]

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 2c121dd7-0ac9-4028-95ad-49f8ee60239a · outbound

This paper cites Modulus-based cascadic multigrid method for quasi-variational inequality problems[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Modulus-based cascadic multigrid method for quasi-variational inequality problems[J]

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 466d4a74-9a16-43d1-b721-cef16091885e · outbound

This paper cites Developing iterative algorithms to solve Sylvester tensor equations[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Developing iterative algorithms to solve Sylvester tensor equations[J]

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 3076a638-bb0d-444a-a9e4-8dd08de1fe1c · outbound

This paper cites Kolda, Brett W.

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Kolda, Brett W

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 0bbf464d-7be6-494c-9f9d-503f50083413 · outbound

This paper cites A projection method to solve linear system in tensor format[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems A projection method to solve linear system in tensor format[J]

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 80191688-c7bf-4e7f-ae23-04129f906f42 · outbound

This paper cites Solution of linear systems in high spatial dimensions[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Solution of linear systems in high spatial dimensions[J]

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 22a1c553-f2f3-4859-a4b9-d624f10fe16b · outbound

This paper cites Mathematical foundation of finite element method[M].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Mathematical foundation of finite element method[M]

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 2a0e919c-4f50-4d4c-a5cc-bf64a5238df7 · outbound

This paper cites Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems[M].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems[M]

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-25T20:47:08.643597Z

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Observation 0f3964a8-f9b7-407b-9a39-7d3433ecd900 · outbound

This paper cites Research on the meshless solving algorithm for 3D steady convection-diffusion problems[J].

An economic cascadic tensor multigrid method for solving high dimensional elliptic linear partial differential problems Research on the meshless solving algorithm for 3D steady convection-diffusion problems[J]

Reference 32

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