Paper Citation Record · LEDGER

Estimating the numerical range with a Krylov subspace

As of 13 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2411.19165.

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

pith.paper-citation-record.v1
2411.19165 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T10:37:09.527150Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T21:16:08.912669Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T20:26:12.138113Z

Reference resolution

35 of 35 outbound references displayed

verified exact0
verified fuzzy24
unresolved11
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9ed1cb9d-dc2f-4d4a-b5dd-07f4babf5462 · outbound

This paper cites The principle of minimized iterations in the solution of the matrix eigenvalue problem.

Estimating the numerical range with a Krylov subspace The principle of minimized iterations in the solution of the matrix eigenvalue problem

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.360902Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6d1c110-8c6b-4a9b-83d3-097429905adc · outbound

This paper cites Computing the field of values and pseudospectra using the lanczos method with continuation.

Estimating the numerical range with a Krylov subspace Computing the field of values and pseudospectra using the lanczos method with continuation

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:10.035088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 924085cc-0c91-46a7-b836-b80fcbfaaca2 · outbound

This paper cites an unresolved cited work.

Estimating the numerical range with a Krylov subspace Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-12T10:37:10.019738Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d4a7f2ae-4adf-4ec5-b33c-30d6a5a6b380 · outbound

This paper cites An elementary proof of a theorem of Johnson and Lindenstrauss.

Estimating the numerical range with a Krylov subspace An elementary proof of a theorem of Johnson and Lindenstrauss

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:10.004795Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 42cd4f07-cc0e-4edb-b956-f8c23b7c0fe8 · outbound

This paper cites Chebfun guide, 2014.

Estimating the numerical range with a Krylov subspace Chebfun guide, 2014

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.382662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acf3237e-463c-4852-b15c-0a17b3dc4437 · outbound

This paper cites Remez-and Nikolskii-type inequalities for logarithmic potentials.SIAM Journal on Mathematical Analysis , 25(2):365–383, 1994.

Estimating the numerical range with a Krylov subspace Remez-and Nikolskii-type inequalities for logarithmic potentials.SIAM Journal on Mathematical Analysis , 25(2):365–383, 1994

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.978777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 11d7fabe-3df1-41df-a382-f7d1aec9f5b9 · outbound

This paper cites The Lanczos algorithm under few iterations: Concentration and location of the output.

Estimating the numerical range with a Krylov subspace The Lanczos algorithm under few iterations: Concentration and location of the output

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.962940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 75d7ae79-8df6-4d2a-ab95-2731486ec384 · outbound

This paper cites Iterative methods for solving linear systems.

Estimating the numerical range with a Krylov subspace Iterative methods for solving linear systems

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.398709Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01a19a53-e232-4835-965d-29e2e202b961 · outbound

This paper cites Convex polytopes , volume 16.

Estimating the numerical range with a Krylov subspace Convex polytopes , volume 16

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.937404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation be7ec2c4-1757-4e56-a535-d97e74af9911 · outbound

This paper cites Methods of conjugate gradients for solving linear systems , vol- ume 49.

Estimating the numerical range with a Krylov subspace Methods of conjugate gradients for solving linear systems , vol- ume 49

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.922208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 738146d9-6b58-47b0-b788-b8aca9bdfb10 · outbound

This paper cites The matrix computation toolbox.

Estimating the numerical range with a Krylov subspace The matrix computation toolbox

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.906685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 306698b3-6283-49e8-8484-511c97880015 · outbound

This paper cites Matrix analysis.

Estimating the numerical range with a Krylov subspace Matrix analysis

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.418698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03835c4c-1fe8-49c9-8526-476286d45979 · outbound

This paper cites Anti-concentration of Gaussian quadratic form.

Estimating the numerical range with a Krylov subspace Anti-concentration of Gaussian quadratic form

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.881292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9c624fca-2c1c-40f0-9ede-9171b04efb55 · outbound

This paper cites The Arnoldi method for normal matrices.

Estimating the numerical range with a Krylov subspace The Arnoldi method for normal matrices

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.866353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ce940066-8b3e-42d9-b868-4adbfe11776d · outbound

This paper cites Numerical determination of the field of values of a general complex matrix.

Estimating the numerical range with a Krylov subspace Numerical determination of the field of values of a general complex matrix

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.850753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ced1bb18-1256-4ebe-be22-9b20a09107b1 · outbound

This paper cites Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start.

Estimating the numerical range with a Krylov subspace Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.835105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8a380325-154b-4e97-8240-43ec878acd6a · outbound

This paper cites An iteration method for the solution of the eigenvalue problem of linear differential and integral operators.

Estimating the numerical range with a Krylov subspace An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.443189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a022eb6f-4152-40a3-a992-f0c451fd0bda · outbound

This paper cites Krylov subspace methods: principles and analysis.

Estimating the numerical range with a Krylov subspace Krylov subspace methods: principles and analysis

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.807423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c1072d68-4389-492e-ac95-a7e0609a9bd7 · outbound

This paper cites Quadratic forms in random variables.

Estimating the numerical range with a Krylov subspace Quadratic forms in random variables

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.792592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e00bc5d1-5cbe-4048-966a-2278496affc7 · outbound

This paper cites SIAM, 2006.

Estimating the numerical range with a Krylov subspace SIAM, 2006

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.777294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 81a31fcc-2b47-45b5-8f67-f4fe1392dcd1 · outbound

This paper cites The Lanczos and conjugate gradient algorithms in finite precision arithmetic.

Estimating the numerical range with a Krylov subspace The Lanczos and conjugate gradient algorithms in finite precision arithmetic

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.762424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8b51b3f6-07c8-4d5a-8577-9f3dc1b29765 · outbound

This paper cites Randomized block Krylov methods for stronger and faster approximate singular value decomposition.

Estimating the numerical range with a Krylov subspace Randomized block Krylov methods for stronger and faster approximate singular value decomposition

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.747245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 49c78ad9-e914-47e9-b9fc-e1054c30e3ea · outbound

This paper cites Solution of sparse indefinite systems of linear equations.

Estimating the numerical range with a Krylov subspace Solution of sparse indefinite systems of linear equations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.470762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b92e6b4b-4a98-46df-bcbf-ac04d4638184 · outbound

This paper cites Approximation of convex sets.

Estimating the numerical range with a Krylov subspace Approximation of convex sets

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.722301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f92aa1cb-ea8d-4b9c-a210-f5e9c643304c · outbound

This paper cites Sur une propri´ et´ e des polynˆ omes de Tchebycheff.Comm.

Estimating the numerical range with a Krylov subspace Sur une propri´ et´ e des polynˆ omes de Tchebycheff.Comm

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.707264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4b4e2bbf-a40b-489a-bcaf-f1f0faf77bb8 · outbound

This paper cites Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems.

Estimating the numerical range with a Krylov subspace Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.691650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d5648821-813d-4b26-8129-c058ba4a458f · outbound

This paper cites Iterative methods for sparse linear systems.

Estimating the numerical range with a Krylov subspace Iterative methods for sparse linear systems

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.489880Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fafd7885-2c1c-4e89-9323-8f084c420ce1 · outbound

This paper cites Numerical methods for large eigenvalue problems: revised edition.

Estimating the numerical range with a Krylov subspace Numerical methods for large eigenvalue problems: revised edition

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.494447Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16decd8e-f499-4dd2-acfc-bd6427f72932 · outbound

This paper cites The origin and development of krylov subspace methods.

Estimating the numerical range with a Krylov subspace The origin and development of krylov subspace methods

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.656261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 50328553-054d-4d78-a3a7-a8e63661b0c2 · outbound

This paper cites Tight query complexity lower bounds for PCA via fi- nite sample deformed Wigner law.

Estimating the numerical range with a Krylov subspace Tight query complexity lower bounds for PCA via fi- nite sample deformed Wigner law

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.640812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ea787a5a-f205-45cd-9f9d-2f77a815fa4c · outbound

This paper cites an unresolved cited work.

Estimating the numerical range with a Krylov subspace Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-12T10:37:09.624899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 34829ec9-1b1e-40d3-8b5e-8a391232f338 · outbound

This paper cites Trefethen.

Estimating the numerical range with a Krylov subspace Trefethen

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.608951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4550666a-a8d6-483e-bda5-51f6dbfb2d5b · outbound

This paper cites Uniform error estimates for the Lanczos method.

Estimating the numerical range with a Krylov subspace Uniform error estimates for the Lanczos method

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.593620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c02c6970-1d47-4981-8866-e3c384f926f9 · outbound

This paper cites High-dimensional statistics: A non-asymptotic viewpoint , volume 48.

Estimating the numerical range with a Krylov subspace High-dimensional statistics: A non-asymptotic viewpoint , volume 48

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-12T10:37:09.522733Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec702448-8996-4549-8b54-a218a3df3863 · outbound

This paper cites A numerical range characterization of jordan blocks.

Estimating the numerical range with a Krylov subspace A numerical range characterization of jordan blocks

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:37:09.566319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation a1b8781f-c478-4949-841e-995f20771688 · inbound

Spectral density estimation for normal matrices cites this paper.

Spectral density estimation for normal matrices Estimating the numerical range with a Krylov subspace

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-01T20:26:12.140364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.