Paper Citation Record · LEDGER

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

As of 16 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:1908.02032.

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

pith.paper-citation-record.v1
1908.02032 v4

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:01:19.625325Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T00:12:47.497020Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-12T00:12:48.139265Z

Reference resolution

33 of 33 outbound references displayed

verified exact9
verified fuzzy7
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7fb26dc6-af9d-48d4-9cdb-f8c5566bbbed · outbound

This paper cites Abramowitz and I.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Abramowitz and I

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:20.039851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 64e798c0-a44f-413d-b2f9-ffd2ce7957da · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:01:20.027829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f1d14766-fcf2-4427-af32-22edf17f790a · outbound

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Beckermann , An error analysis for rational Galerkin projection applied to the Sylvester equation , SIAM J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.519124Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0258e092-7b40-4503-8735-68c6d912077c · outbound

This paper cites Beckermann and L.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Beckermann and L

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.522555Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3b84447-bbef-4a26-a1fc-d15171fd213b · outbound

This paper cites Beckermann and A.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Beckermann and A

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.526160Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation feaa002a-29b7-4407-a3b2-48f8e3b0eca6 · outbound

This paper cites Benner, R.-C.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Benner, R.-C

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.529667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13d94d90-71a7-4704-b52f-1ed877226f00 · outbound

This paper cites Benzi and C.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Benzi and C

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:20.017451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a12e3b01-acf1-4fcf-b011-b82a16f6bf15 · outbound

This paper cites Benzi and V.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Benzi and V

Reference 8

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.787454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9272c8dc-f25d-4e40-a718-8091b85f0183 · outbound

This paper cites Berg , Stieltjes-Pick-Bernstein-Schoenberg and their connecti on to complete monotonicity , Positive Def- inite Functions: From Schoenberg to Space-Time Challenges , (2008), pp.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Berg , Stieltjes-Pick-Bernstein-Schoenberg and their connecti on to complete monotonicity , Positive Def- inite Functions: From Schoenberg to Space-Time Challenges , (2008), pp

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:20.006682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9ae564d6-c417-40dd-b7bb-b456eef70d08 · outbound

This paper cites Bernstein , Sur les fonctions absolument monotones , Acta Math., 52 (1929), pp.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Bernstein , Sur les fonctions absolument monotones , Acta Math., 52 (1929), pp

Reference 10

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.777820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 57ba36be-38e0-49db-b154-690357e6178b · outbound

This paper cites Braess , Nonlinear approximation theory , vol.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Braess , Nonlinear approximation theory , vol

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:19.994952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9176332b-f83c-47a7-9faa-1a661f2d451b · outbound

This paper cites Breiten, V.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Breiten, V

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.552702Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0382ec70-a2ea-49ff-82c2-e9ca87f3768b · outbound

This paper cites Druskin and L.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Druskin and L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:19.976515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 59fd7100-6906-4cb3-8a9a-c1fd964135f3 · outbound

This paper cites Druskin, L.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Druskin, L

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.560015Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da91e9e8-9041-40ec-8e43-05614a4a65ed · outbound

This paper cites Druskin, C.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Druskin, C

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:19.963122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ed8d1c03-08e1-4472-a009-8fe8a6d79fdd · outbound

This paper cites Druskin and V.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Druskin and V

Reference 16

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.759043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2b30920b-b68a-4cd0-a8d2-51c08312beda · outbound

This paper cites Frommer, S.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Frommer, S

Reference 17

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.747058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cbe6d75d-2bc6-4218-b159-fb4bac391a4e · outbound

This paper cites G ¨uttel, Rational Krylov approximation of matrix functions: numeri cal methods and optimal pole se- lection, GAMM-Mitt., 36 (2013), pp.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection G ¨uttel, Rational Krylov approximation of matrix functions: numeri cal methods and optimal pole se- lection, GAMM-Mitt., 36 (2013), pp

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.573574Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8df4241-13bb-4aad-b9c6-9ca26db53b84 · outbound

This paper cites G ¨uttel and L.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection G ¨uttel and L

Reference 19

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.729554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2700a458-0dce-4565-a3ab-8e719debbf4f · outbound

This paper cites Hochbruck and A.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Hochbruck and A

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.579902Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7edda0ed-8da0-4871-bd0c-ab2f0bcbc960 · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 21

Resolution: verified exact; raw_fallback, observed 2026-08-14T15:01:19.906445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 02bcc78e-df44-41c6-ac3d-f749f4fae091 · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:01:19.950177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5942879c-6afc-4004-ada8-99c79a4bb2a6 · outbound

This paper cites Kressner, S.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Kressner, S

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.589148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19fe7b6e-5c0c-4eb6-8915-97e47bc0a809 · outbound

This paper cites Massei, M.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Massei, M

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.592169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18d59f18-d673-40ad-bcc9-e65aa4891c87 · outbound

This paper cites Massei, D.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Massei, D

Reference 25

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.699072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b602e64a-51fe-45da-9aaf-237ad56d1cfb · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 26

Resolution: verified exact; doi, observed 2026-08-14T15:01:19.686576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eb084336-00c0-4bab-b0e3-1c7b071876f1 · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:01:19.940515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 54024047-e0f4-4891-b7ec-a9206ee5fc61 · outbound

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Simoncini , Computational methods for linear matrix equations , SIAM Rev., 58 (2016), pp

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.605722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b01eab3-0c1c-425c-8856-10a71cc6315a · outbound

This paper cites Accelerated filtering on graphs using Lanczos method.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Accelerated filtering on graphs using Lanczos method

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-14T15:01:19.829308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d5ff881d-0065-489a-b5e8-b35087e33d29 · outbound

This paper cites Townsend and S.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Townsend and S

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.613448Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8eecfd10-5419-4a70-9cc5-c5ecaaeb0a25 · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:01:19.929234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d8c2de5b-7f5b-4265-953b-c975cf7a8c23 · outbound

This paper cites an unresolved cited work.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-14T15:01:19.621181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73f514de-1ad5-4582-88b5-09a20ea31d65 · outbound

This paper cites Zolotarev , Application of elliptic functions to questions of function s deviating least and most from zero, Zap.

Rational Krylov for Stieltjes matrix functions: convergence and pole selection Zolotarev , Application of elliptic functions to questions of function s deviating least and most from zero, Zap

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:01:19.917924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 89f952dd-98e1-4a03-8382-287add99dbc0 · inbound

A Shared Observation Shields Collective Fluctuations while Preserving Local Independence cites this paper.

A Shared Observation Shields Collective Fluctuations while Preserving Local Independence Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Reference 118

Resolution: metadata mismatch; local_arxiv, observed 2026-08-12T00:12:48.144140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.