Paper Citation Record · LEDGER

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems

As of 21 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 1 inbound Pith citation observation for arXiv:2509.07179.

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

pith.paper-citation-record.v1
2509.07179 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:25:19.263865Z

measured 41 of 41 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T18:29:27.386149Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

40 of 40 outbound references displayed

verified exact1
verified fuzzy23
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ba13b5ac-1c5d-4111-aa6b-fc25c8522f54 · outbound

This paper cites Ayuso de Dios, F.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Ayuso de Dios, F

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.827906Z

Source-reported events for the cited work

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

Observation cf04d572-8dfe-4548-8c99-e1f10b373150 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.815227Z

Source-reported events for the cited work

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

Observation 67799d73-7d56-4320-9cb6-a0b40ec23f54 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.803353Z

Source-reported events for the cited work

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

Observation 03e4e4c9-fce1-4cf0-bce1-868a84652d9f · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T16:25:19.120338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b5b780b-c7c1-43ca-a80f-83166a93ac17 · outbound

This paper cites Budisa, W.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Budisa, W

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.782068Z

Source-reported events for the cited work

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

Observation 2a7819e5-8d6a-4be2-aa29-e9978602332f · outbound

This paper cites Cao , On the convergence of general stationary linear iterative methods for singular linear systems , SIAM J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Cao , On the convergence of general stationary linear iterative methods for singular linear systems , SIAM J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.770534Z

Source-reported events for the cited work

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

Observation 3a38e64a-fc03-4beb-af9e-208408da1ba8 · outbound

This paper cites Chen , Deriving the X -- Z identity from auxiliary space method , in Domain Decomposition Methods in Science and Engineering XIX , vol.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Chen , Deriving the X -- Z identity from auxiliary space method , in Domain Decomposition Methods in Science and Engineering XIX , vol

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.759249Z

Source-reported events for the cited work

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

Observation 4675b7a3-2c2f-450d-b5be-741df5a624dc · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.748653Z

Source-reported events for the cited work

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

Observation 86a3b406-69c0-4b5e-8533-0153af559280 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.737493Z

Source-reported events for the cited work

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

Observation 1e3b1694-9fae-4cde-93b2-dec8a9618aa3 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.725113Z

Source-reported events for the cited work

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

Observation dafaf5ca-409a-488d-9ddc-850683cb3976 · outbound

This paper cites Gopalakrishnan, M.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Gopalakrishnan, M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.713146Z

Source-reported events for the cited work

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

Observation 54f2b399-b7d3-4ed2-b1b3-fb7f81f1f13b · outbound

This paper cites Grasedyck, L.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Grasedyck, L

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.701315Z

Source-reported events for the cited work

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

Observation 8894cd26-d000-4ec0-8bcc-54fd83572008 · outbound

This paper cites Convergence of the Conjugate Gradient Method on Singular Systems.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Convergence of the Conjugate Gradient Method on Singular Systems

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:25:19.387660Z

Source-reported events for the cited work

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

Observation 7adb351d-81b5-4665-98b9-9fbdaa647fe5 · outbound

This paper cites Hiptmair , Finite elements in computational electromagnetism , Acta Numer., 11 (2002), pp.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Hiptmair , Finite elements in computational electromagnetism , Acta Numer., 11 (2002), pp

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.688813Z

Source-reported events for the cited work

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

Observation b4c4c97b-52af-42bf-942b-b6ca2e445b0b · outbound

This paper cites Hiptmair and J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Hiptmair and J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.677300Z

Source-reported events for the cited work

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

Observation db8e800d-2b26-4ede-841b-5ecb1725a344 · outbound

This paper cites Hiptmair and J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Hiptmair and J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.665231Z

Source-reported events for the cited work

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

Observation f797baee-82ae-49f4-9ccf-12d1f00bed16 · outbound

This paper cites Hu , Convergence of the H iptmair-- X u preconditioner for M axwell's equations with jump coefficients (i): E xtensions of the regular decomposition , SIAM J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Hu , Convergence of the H iptmair-- X u preconditioner for M axwell's equations with jump coefficients (i): E xtensions of the regular decomposition , SIAM J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.654793Z

Source-reported events for the cited work

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

Observation 655c128c-e438-48ac-b0b9-d564f9c88a51 · outbound

This paper cites Hu , Convergence of the H iptmair-- X u preconditioner for H ( curl ) -elliptic problems with jump coefficients (ii): M ain results , SIAM J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Hu , Convergence of the H iptmair-- X u preconditioner for H ( curl ) -elliptic problems with jump coefficients (ii): M ain results , SIAM J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.644124Z

Source-reported events for the cited work

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

Observation 1f4987cd-313f-4261-a6eb-74b549f2b032 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.632742Z

Source-reported events for the cited work

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

Observation 5c94c30a-0785-47ad-b579-2fe7a1fefe74 · outbound

This paper cites Subspace correction as a general framework for convex optimization algorithms.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Subspace correction as a general framework for convex optimization algorithms

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T16:25:19.188614Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 27556bf6-ebb0-4ae8-9446-9a00ad5fb707 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.620341Z

Source-reported events for the cited work

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

Observation 73536bb8-36e2-46c7-a143-1aac0db3a16d · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.608549Z

Source-reported events for the cited work

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

Observation fce96fa2-315a-4c75-837d-053b52c3ba41 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.596814Z

Source-reported events for the cited work

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

Observation 8d65b7b5-2778-45f5-a0d6-69e9caa8dd30 · outbound

This paper cites Lee and J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Lee and J

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T16:25:19.203075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8320f3c6-8947-4e37-83b4-b48a4d350e60 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.584518Z

Source-reported events for the cited work

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

Observation 0a6d8dfd-95b0-493b-9b82-d0e3f8baa1b8 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.572199Z

Source-reported events for the cited work

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

Observation 85a93d79-7625-441d-844e-2fcb79ddff1c · outbound

This paper cites Li and X.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Li and X

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.561243Z

Source-reported events for the cited work

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

Observation 0e71a60b-d3b9-4b97-944f-5dcc38a6bd1d · outbound

This paper cites Lions , On the S chwarz alternating method.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Lions , On the S chwarz alternating method

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.549040Z

Source-reported events for the cited work

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

Observation 262bc032-7c08-4779-a548-f03bafa711d4 · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.534474Z

Source-reported events for the cited work

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

Observation b19991fe-18f4-4179-b9b6-edf9d1356202 · outbound

This paper cites Park , Additive S chwarz methods for convex optimization as gradient methods , SIAM J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Park , Additive S chwarz methods for convex optimization as gradient methods , SIAM J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.522552Z

Source-reported events for the cited work

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

Observation 2a829245-e816-4eca-aefd-224b2bec9e60 · outbound

This paper cites Saad , Iterative Methods for Sparse Linear Systems , SIAM, Philadelphia, PA, second ed., 2003.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Saad , Iterative Methods for Sparse Linear Systems , SIAM, Philadelphia, PA, second ed., 2003

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.509255Z

Source-reported events for the cited work

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

Observation 6d78b879-0266-44e6-92c2-966bfe890c27 · outbound

This paper cites Toselli and O.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Toselli and O

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.496929Z

Source-reported events for the cited work

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

Observation 06e6e0dc-fdb4-4f49-bc9f-9912cc3449cd · outbound

This paper cites an unresolved cited work.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:25:19.485423Z

Source-reported events for the cited work

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

Observation d8f0f25c-4f69-4847-a39f-d7440a3c9f1f · outbound

This paper cites Wu, Y.-J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Wu, Y.-J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.473353Z

Source-reported events for the cited work

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

Observation e70399bf-d13f-47b4-8ecc-5319680833c1 · outbound

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

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Xu , Iterative methods by space decomposition and subspace correction , SIAM Rev., 34 (1992), pp

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.461637Z

Source-reported events for the cited work

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

Observation b709a91f-db9c-4a78-8917-031e2fa24aaf · outbound

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

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Xu , The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids , Computing, 56 (1996), pp

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.449612Z

Source-reported events for the cited work

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

Observation 9880b9d6-d7df-4e9f-9d04-1347745f5e35 · outbound

This paper cites Xu and L.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Xu and L

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.436682Z

Source-reported events for the cited work

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

Observation e9ec4a8d-5972-457d-a150-9eccf3f7f2b5 · outbound

This paper cites Xu and L.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Xu and L

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.423817Z

Source-reported events for the cited work

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

Observation c8a0e8a4-42da-4bb4-8d30-d2fa0c2947aa · outbound

This paper cites Zhang and J.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Zhang and J

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.411813Z

Source-reported events for the cited work

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

Observation dd591c5d-7011-4a9d-8dd2-1e2669f2c7f2 · outbound

This paper cites Zhang , Multilevel S chwarz methods , Numer.

Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems Zhang , Multilevel S chwarz methods , Numer

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:25:19.399367Z

Source-reported events for the cited work

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

Pith citing papers

Observation f08bb0da-256a-490d-b21b-c1a061b24d76 · inbound

A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners cites this paper.

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

Resolution: unresolved; no resolver link, observed 2026-08-03T18:29:27.386149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.