Paper Citation Record · LEDGER

Lanczos with compression for symmetric matrix Lyapunov equations

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2505.22498.

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

pith.paper-citation-record.v1
2505.22498 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:15:29.155580Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

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

Source: cited_works

Reference resolution

37 of 37 outbound references displayed

verified exact1
verified fuzzy25
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 50711c2a-37b3-4b37-8da2-e94cfe9f8f4f · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:36.658345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 28a41f64-c212-43db-8866-5ccff1f03c64 · outbound

This paper cites Beckermann, An error analysis for rational Galerkin projection applied to the Sylvester equation, SIAM J.

Lanczos with compression for symmetric matrix Lyapunov equations Beckermann, An error analysis for rational Galerkin projection applied to the Sylvester equation, SIAM J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:36.380847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0606bb05-5def-4f83-a7b2-625ecbf6805f · outbound

This paper cites Beckermann, A.

Lanczos with compression for symmetric matrix Lyapunov equations Beckermann, A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:36.129394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 043d5d61-fb29-4163-a31a-d9a61d35307f · outbound

This paper cites Beckermann and A.

Lanczos with compression for symmetric matrix Lyapunov equations Beckermann and A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:35.988893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c92266c3-febf-43a6-8f53-f227a3592bc2 · outbound

This paper cites Benner, A.

Lanczos with compression for symmetric matrix Lyapunov equations Benner, A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:35.776125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 94c17b6c-03ae-4596-8588-87910d0ca1cf · outbound

This paper cites Benner, R.-C.

Lanczos with compression for symmetric matrix Lyapunov equations Benner, R.-C

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:35.563816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7b65d486-9a5b-4d0d-9483-4b7e00e9421d · outbound

This paper cites Benner, V.

Lanczos with compression for symmetric matrix Lyapunov equations Benner, V

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:35.384398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9bf1a258-14c4-483a-bf10-99dc816ede3c · outbound

This paper cites Benner, D.

Lanczos with compression for symmetric matrix Lyapunov equations Benner, D

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:35.107229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 44f99169-d97b-4750-adc9-587f86d6decd · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:34.862817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3beb5559-1730-46fb-9f53-44741fcf750f · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:34.638541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fd33303f-7ff0-4b22-bc05-becdae0d92b6 · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:34.355791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2d333f87-cb35-4d01-8a45-f94a785d7468 · outbound

This paper cites A low-memory Lanczos method with rational Krylov compression for matrix functions.

Lanczos with compression for symmetric matrix Lyapunov equations A low-memory Lanczos method with rational Krylov compression for matrix functions

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:15:29.342999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8d29b038-7cc2-4b97-a631-81ae48d5e911 · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:34.107381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b70db9de-7cf5-4aad-91f1-b1df0ae0f27e · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:33.893005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4e705247-7d51-4f49-b9e6-ece11f8c94cc · outbound

This paper cites Druskin, A.

Lanczos with compression for symmetric matrix Lyapunov equations Druskin, A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:33.665197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 662ce37f-96e0-4d7d-88ee-af273ed30e7a · outbound

This paper cites Druskin, L.

Lanczos with compression for symmetric matrix Lyapunov equations Druskin, L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:33.431385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 93a8b397-2c36-44b4-b13e-c996f8b8609b · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:33.253591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0d59987f-06cc-4dea-a9b1-cb9b171bd8f3 · outbound

This paper cites Elsworth and S.

Lanczos with compression for symmetric matrix Lyapunov equations Elsworth and S

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:33.094670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f89ba20e-cdce-45bc-b2d2-345a695d7b0c · outbound

This paper cites Gajic and M.

Lanczos with compression for symmetric matrix Lyapunov equations Gajic and M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:32.916432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5f0382ac-cd6d-4daf-b118-5d469cc8f6dc · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:32.659141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7ce8a679-e009-4fc0-a5a3-c110fba5fdfc · outbound

This paper cites Grubišić and D.

Lanczos with compression for symmetric matrix Lyapunov equations Grubišić and D

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:32.447095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 34cdb9e1-b010-4bea-bd75-75ec48c3822b · outbound

This paper cites Güttel, Rational Krylov Methods for Operator Functions, PhD thesis, Technische Uni- versität Bergakademie Freiberg, Germany, 2010.

Lanczos with compression for symmetric matrix Lyapunov equations Güttel, Rational Krylov Methods for Operator Functions, PhD thesis, Technische Uni- versität Bergakademie Freiberg, Germany, 2010

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:32.278501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ba596b2a-8ed5-4ee8-9328-acc3756e2eb9 · outbound

This paper cites Güttel, D.

Lanczos with compression for symmetric matrix Lyapunov equations Güttel, D

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:32.094997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eb1cdd80-53e6-4fe4-a1e6-181e35c454e1 · outbound

This paper cites Güttel and M.

Lanczos with compression for symmetric matrix Lyapunov equations Güttel and M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:31.950936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 11850c74-8382-4633-a758-0ccfbfa95052 · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:31.775090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e95bab3a-f609-41cb-acb3-7cb2432bdde1 · outbound

This paper cites Jbilou and A.

Lanczos with compression for symmetric matrix Lyapunov equations Jbilou and A

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:31.598570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d56cc17d-3aa2-49f8-baf5-156220dd3a99 · outbound

This paper cites Kressner, Memory-efficient Krylov subspace techniques for solving large-scale Lyapunov equations, in 2008 IEEE International Conference on Computer-Aided Control Systems, 2008.

Lanczos with compression for symmetric matrix Lyapunov equations Kressner, Memory-efficient Krylov subspace techniques for solving large-scale Lyapunov equations, in 2008 IEEE International Conference on Computer-Aided Control Systems, 2008

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:31.358236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6d9096c3-c3db-413e-9d3c-9e3890786be6 · outbound

This paper cites Kressner, K.

Lanczos with compression for symmetric matrix Lyapunov equations Kressner, K

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:31.154478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 587059cb-4c26-45a9-ac57-904622e3a884 · outbound

This paper cites Li and J.

Lanczos with compression for symmetric matrix Lyapunov equations Li and J

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:30.890700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation db23b641-a549-494e-b55a-247b00af1dc5 · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:30.677826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5b3ccfba-0ebf-4251-a1a7-78b3f7634d62 · outbound

This paper cites an unresolved cited work.

Lanczos with compression for symmetric matrix Lyapunov equations Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:15:30.513552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bfe19886-17a8-4ee5-aefd-dd23734123d1 · outbound

This paper cites Matrix Anal.

Lanczos with compression for symmetric matrix Lyapunov equations Matrix Anal

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:30.274508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6d6d6a25-e989-4e1d-86de-dbf1afbfe8f3 · outbound

This paper cites Palitta and V.

Lanczos with compression for symmetric matrix Lyapunov equations Palitta and V

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:30.113884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 882e3995-09bc-49ad-90ee-d3d8385649a9 · outbound

This paper cites Penzl , A cyclic low-rank Smith method for large sparse Lyapunov equations, SIAM J.

Lanczos with compression for symmetric matrix Lyapunov equations Penzl , A cyclic low-rank Smith method for large sparse Lyapunov equations, SIAM J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:29.948397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 026ad400-e5af-4193-aad6-749be54630a5 · outbound

This paper cites Saad , Numerical solution of large Lyapunov equations, in Signal processing, scattering and operator theory, and numerical methods (Amsterdam, 1989), vol.

Lanczos with compression for symmetric matrix Lyapunov equations Saad , Numerical solution of large Lyapunov equations, in Signal processing, scattering and operator theory, and numerical methods (Amsterdam, 1989), vol

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:29.823750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a7053985-b1e9-4ee2-8c90-4cae649c4413 · outbound

This paper cites Simoncini , Computational methods for linear matrix equations, SIAM Rev., 58 (2016), pp.

Lanczos with compression for symmetric matrix Lyapunov equations Simoncini , Computational methods for linear matrix equations, SIAM Rev., 58 (2016), pp

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:29.669615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ed8aaf7c-8d21-455d-8a0f-fdfdd274c20d · outbound

This paper cites Simoncini and V.

Lanczos with compression for symmetric matrix Lyapunov equations Simoncini and V

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:15:29.525481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

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