Paper Citation Record · LEDGER

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners

As of 22 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 2 inbound Pith citation observations for arXiv:2512.06166.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2512.06166 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T18:29:28.282071Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-08T03:32:06.931610Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-08T03:34:32.413834Z

Reference resolution

41 of 41 outbound references displayed

verified exact1
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External citation measurements

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Outbound references

Observation 04c9838c-0064-4512-b357-0b26d1be59a2 · outbound

This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 1

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Observation 5efdd876-a698-4745-aa44-54c93634bba7 · outbound

This paper cites Bebendorf , A note on the P oincar\' e inequality for convex domains , Z.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Bebendorf , A note on the P oincar\' e inequality for convex domains , Z

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T18:29:24.821882Z

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Observation e4fdb806-5bc5-4a05-8477-dc8d785cd54a · outbound

This paper cites Bey , Simplicial grid refinement: O n F reudenthal's algorithm and the optimal number of congruence classes , Numer.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Bey , Simplicial grid refinement: O n F reudenthal's algorithm and the optimal number of congruence classes , Numer

Reference 3

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Observation 65abff56-5ec5-4235-a7e7-08a67358d162 · outbound

This paper cites Bornemann and H.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Bornemann and H

Reference 4

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This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 5

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This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 6

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Observation 888fcff2-4f04-4a05-ae4d-ab2a23346778 · outbound

This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 7

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This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 8

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Observation e5a816c8-5183-4c76-85d1-5b6fe088207e · outbound

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 9

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This paper cites Buffa, H.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Buffa, H

Reference 10

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 12

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Observation d32d349d-b7fa-446d-9cf1-5d29b96aecb3 · outbound

This paper cites Cl\'ement , Approximation by finite element functions using local regularization , Rev.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Cl\'ement , Approximation by finite element functions using local regularization , Rev

Reference 13

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This paper cites Dahmen and A.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Dahmen and A

Reference 14

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Deiml and D

Reference 15

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Observation c78db366-aa78-4531-b333-da004b7e999d · outbound

This paper cites Dekel and D.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Dekel and D

Reference 16

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Ern and J.-L

Reference 17

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 18

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Observation e9db5341-ad28-473a-a626-b8e229d65966 · outbound

This paper cites Faustmann, J.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Faustmann, J

Reference 19

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Observation 55061e43-1632-48bf-8643-bfef064560ca · outbound

This paper cites Grisvard , Elliptic Problems in Nonsmooth Domains , Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Grisvard , Elliptic Problems in Nonsmooth Domains , Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011

Reference 20

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This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 21

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Observation 6a7a5785-b5f7-4314-b02a-c07477e34999 · outbound

This paper cites Izumi , Sufficiency of simplex inequalities , Proc.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Izumi , Sufficiency of simplex inequalities , Proc

Reference 22

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Quantum preconditioning method for finite difference discretizations of the Poisson equation via Schr\"odingerization

Reference 23

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Schr\"odingerization based quantum algorithms for the fractional Poisson equation

Reference 24

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 25

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Observation dd4abd36-80c2-4f72-9523-377e77970c50 · outbound

This paper cites Li and X.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Li and X

Reference 26

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Observation 06b80a4b-b870-4137-b124-ca5cb8ea172d · outbound

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Maugeri, D

Reference 27

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Observation 4233dc6e-3a73-49db-9fd4-3b174852a15b · outbound

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Montanaro and S

Reference 28

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Observation 5b555a49-0183-4663-afdd-1e6b3f4e0c2f · outbound

This paper cites Oswald , On function spaces related to finite element approximation theory , Z.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Oswald , On function spaces related to finite element approximation theory , Z

Reference 29

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This paper cites Park , Two-level overlapping S chwarz preconditioners with universal coarse spaces for 2m th-order elliptic problems , SIAM J.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Park , Two-level overlapping S chwarz preconditioners with universal coarse spaces for 2m th-order elliptic problems , SIAM J

Reference 30

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems

Reference 31

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 32

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This paper cites an unresolved cited work.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Unresolved cited work

Reference 33

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Observation 3bdfc759-ebcf-4724-ab64-606be6167870 · outbound

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Veeser and R

Reference 34

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Observation 772b3ca9-5bb4-40fa-92e0-cbbb398bd0db · outbound

This paper cites Xu , Theory of multilevel methods , ProQuest LLC, Ann Arbor, MI, 1989.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Xu , Theory of multilevel methods , ProQuest LLC, Ann Arbor, MI, 1989

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T18:29:27.819928Z

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Observation ad96c243-9289-482e-b4ee-cb42bbc0fef4 · outbound

This paper cites Xu , Counterexamples concerning a weighted L ^2 projection , Math.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Xu , Counterexamples concerning a weighted L ^2 projection , Math

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T18:29:27.892128Z

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Observation 4cc69292-9d1b-40a1-8482-8db0dc562914 · outbound

This paper cites Xu , Iterative methods by space decomposition and subspace correction , SIAM Rev., 34 (1992), pp.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Xu , Iterative methods by space decomposition and subspace correction , SIAM Rev., 34 (1992), pp

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T18:29:27.965142Z

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Observation dbfc03b5-4b8a-4e76-8177-09b1acb5ee94 · outbound

This paper cites Xu , The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids , Computing, 56 (1996), pp.

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Xu , The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids , Computing, 56 (1996), pp

Reference 38

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Observation a08ea4aa-370d-4321-adaa-4616517c109e · outbound

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Xu and L

Reference 39

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners Zhang , Divergence-free finite elements on tetrahedral grids for k 6 , Math

Reference 40

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A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners write newline

Reference 41

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Pith citing papers

Observation 23a318de-55a1-4f00-8096-799c0c09e27a · inbound

Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation cites this paper.

Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners

Reference 24

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0d04f70c-d07a-4216-b455-7f6836f8028c · inbound

Quantum-inspired methods for finite-element discretizations of the high-dimensional Poisson equation cites this paper.

Quantum-inspired methods for finite-element discretizations of the high-dimensional Poisson equation A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners

Reference 3

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