Paper Citation Record · LEDGER

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions

As of 5 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2605.12801.

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pith.paper-citation-record.v1
2605.12801 v1

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measured 42 of 42 reference resolution

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42 of 42 outbound references displayed

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Outbound references

Observation c7c247a2-9356-4b5d-a6f2-7524d846100c · outbound

This paper cites Al-Mohy and Nicholas J.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Al-Mohy and Nicholas J

Reference 1

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.190047Z

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Observation 06c26f39-a66a-4168-a150-49d44889982e · outbound

This paper cites Learning quantum systems.Nature Reviews Physics, 5:141–156.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Learning quantum systems.Nature Reviews Physics, 5:141–156

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.690249Z

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Observation 574aedc3-4057-4515-8081-799db9f53670 · outbound

This paper cites Error estimates and evaluation of matrix functions via the Faber transform.SIAM Journal on Numerical Analysis, 47(5):3849–3883.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Error estimates and evaluation of matrix functions via the Faber transform.SIAM Journal on Numerical Analysis, 47(5):3849–3883

Reference 3

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.205178Z

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Observation 50f24d10-3f88-465b-8dc2-7b5394154df4 · outbound

This paper cites Matrix functions in network analysis.GAMM-Mitteilungen, 43 (3):e202000012.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Matrix functions in network analysis.GAMM-Mitteilungen, 43 (3):e202000012

Reference 4

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Observation 6c6556be-4d62-4031-bf35-5bbe51cf8547 · outbound

This paper cites Krylov-aware stochastic trace estimation.SIAM Journal on Matrix Analysis and Applications, 44(3):1218–1244.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Krylov-aware stochastic trace estimation.SIAM Journal on Matrix Analysis and Applications, 44(3):1218–1244

Reference 5

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.315553Z

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Observation 2442b2c7-827c-4903-b4ba-20f62146aad6 · outbound

This paper cites A bivariate extension of the Crouzeix-Palencia result with an application to Fr\'echet derivatives of matrix functions.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions A bivariate extension of the Crouzeix-Palencia result with an application to Fr\'echet derivatives of matrix functions

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:32:51.643944Z

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Observation fb9264a9-185d-4db6-9a0f-fcd8bdaf2b51 · outbound

This paper cites an unresolved cited work.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 7

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Observation 0940260c-4bad-436e-9ff1-97e13fb47314 · outbound

This paper cites Communication in complex networks.Applied Numerical Mathematics, 172:186–205.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Communication in complex networks.Applied Numerical Mathematics, 172:186–205

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.789288Z

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Observation d6fdb7ce-3a32-4d24-80f6-fe38eeb6aa0f · outbound

This paper cites Scal- able log determinants for gaussian process kernel learning.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Scal- able log determinants for gaussian process kernel learning

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.699492Z

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Observation c6af202a-3968-43b5-994f-d3f238628af7 · outbound

This paper cites Elman, David J.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Elman, David J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.780830Z

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Observation 970a5b9a-cb56-4fe2-80ae-ebdee6abd3dc · outbound

This paper cites Efficient solution of parabolic equations by Krylov approximation methods.SIAM Journal on Scientific and Statistical Computing, 13(5):1236– 1264.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Efficient solution of parabolic equations by Krylov approximation methods.SIAM Journal on Scientific and Statistical Computing, 13(5):1236– 1264

Reference 11

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.297177Z

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Observation fe3ca0f3-b9ff-4835-844e-828a235fdc73 · outbound

This paper cites Weinberger, David Bindel, and Andrew Gordon Wilson.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Weinberger, David Bindel, and Andrew Gordon Wilson

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.784833Z

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Observation d570c17c-c0bb-4874-852b-be4e551d44fd · outbound

This paper cites Golub and Gérard Meurant.Matrices, Moments and Quadrature with Applications.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Golub and Gérard Meurant.Matrices, Moments and Quadrature with Applications

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.793918Z

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Observation abf7eee7-63ad-4896-865d-f7dfeaed7d03 · outbound

This paper cites Golub and Charles F.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Golub and Charles F

Reference 14

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Observation 50b7b874-4f3a-468e-a18c-f57fa16c746c · outbound

This paper cites Practical hamiltonian learning with unitary dynamics and gibbs states.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Practical hamiltonian learning with unitary dynamics and gibbs states

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.767269Z

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Observation 2ba8c0bd-c00c-48ea-8c29-b1e8cf32bccd · outbound

This paper cites J.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions J

Reference 16

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Observation 56da1474-c327-4779-8d3f-ac64923f6561 · outbound

This paper cites Hochbruck and C.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Hochbruck and C

Reference 17

Resolution: metadata mismatch; doi, observed 2026-05-14T19:32:50.231535Z

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Observation afa0f382-376b-4332-9aad-fae173a36455 · outbound

This paper cites Robust and efficient hamiltonian learning.Quantum, 7:1045.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Robust and efficient hamiltonian learning.Quantum, 7:1045

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.776782Z

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Observation 3ac641e7-57b1-47a4-aa13-ae4169f965ff · outbound

This paper cites Hutchinson , A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines, Communications in Statistics - Simulation and Computation, 18 (1989), pp.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Hutchinson , A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines, Communications in Statistics - Simulation and Computation, 18 (1989), pp

Reference 19

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.267553Z

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Observation 28a655d6-9164-4143-97f9-48bca89a81ad · outbound

This paper cites Scalable marginal likelihood estimation for model selection in deep learning.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Scalable marginal likelihood estimation for model selection in deep learning

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.762740Z

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Observation a938f93e-e762-438b-a850-6f24c77a482c · outbound

This paper cites Relton, and Marcel Schweitzer.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Relton, and Marcel Schweitzer

Reference 21

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.273287Z

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Observation 513aefca-2445-4ac1-b0d3-66ae488443eb · outbound

This paper cites Gradients of functions of large matrices.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Gradients of functions of large matrices

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.798336Z

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Observation 4fcb06f5-5b45-4a47-a853-6f6830618261 · outbound

This paper cites A krylov subspace method for the approximation of bivariate matrix functions.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions A krylov subspace method for the approximation of bivariate matrix functions

Reference 23

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.212675Z

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Observation c78f2d69-3c0f-4f3d-90d0-fb5c98fa727b · outbound

This paper cites A novel krylov subspace method for approximating Fréchet derivatives of large-scale matrix functions.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions A novel krylov subspace method for approximating Fréchet derivatives of large-scale matrix functions

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:32:51.637688Z

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Observation cc8b9348-16a3-4daf-8769-440ad908df70 · outbound

This paper cites Deep learning via hessian-free optimization.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Deep learning via hessian-free optimization

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.735015Z

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Observation 61f33db8-61ca-41fd-86ca-c69ed7e5c645 · outbound

This paper cites SIAM.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions SIAM

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.739757Z

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Observation a549cad2-750e-4131-af83-e486400dbc1b · outbound

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Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:32:50.241412Z

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Observation ccff401d-f247-4219-805d-a8b2ffbc3138 · outbound

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Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-05-14T19:32:52.694604Z

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Observation 43f006f0-a4a2-4c90-b55b-b6535c62242a · outbound

This paper cites an unresolved cited work.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-14T19:32:52.725468Z

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Observation e1131e8a-080d-4057-80fc-f5fa79c3f647 · outbound

This paper cites PhD thesis, University of London.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions PhD thesis, University of London

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.730528Z

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Observation 5197a4f8-f160-44b9-8275-4f97eba12a9d · outbound

This paper cites Parlett.The Symmetric Eigenvalue Problem.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Parlett.The Symmetric Eigenvalue Problem

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.758271Z

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Observation 13af7d53-7b63-4602-92a2-610639c9d42e · outbound

This paper cites Parlett and David S.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Parlett and David S

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T19:32:52.717547Z

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Observation 500e5c32-91b9-4dc7-9136-16bb50ca210b · outbound

This paper cites On the stability of network indices defined by means of matrix functions.SIAM Journal on Matrix Analysis and Applications, 39(4):1521–1546.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions On the stability of network indices defined by means of matrix functions.SIAM Journal on Matrix Analysis and Applications, 39(4):1521–1546

Reference 34

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.251463Z

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Observation 8ab46ee2-22e3-49a2-b4ec-b5f92364c1bb · outbound

This paper cites Physicochemical properties of protein tertiary structure.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Physicochemical properties of protein tertiary structure

Reference 35

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.285522Z

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Observation 8eaba314-5f90-4d7e-a431-799954987a67 · outbound

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Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 36

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Observation ad28f8fb-e067-42ee-b155-474f3dbdac2b · outbound

This paper cites Rue , author L.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Rue , author L

Reference 37

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Observation 4f59fb77-7e76-46ed-8406-3047f348812d · outbound

This paper cites Saad, Analysis of some krylov subspace ap- proximations to the matrix exponential operator, SIAM Journal on Numerical Analysis 29, 209 (1992) , https://doi.org/10.1137/0729014.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Saad, Analysis of some krylov subspace ap- proximations to the matrix exponential operator, SIAM Journal on Numerical Analysis 29, 209 (1992) , https://doi.org/10.1137/0729014

Reference 38

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.259061Z

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Observation d889b171-6d59-4372-b89b-a2e35e97f3b4 · outbound

This paper cites Saad, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Saad, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics

Reference 39

Resolution: metadata mismatch; doi, observed 2026-05-14T19:32:50.225951Z

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Observation 2840e78e-f662-4db4-b61f-2814b93a60c3 · outbound

This paper cites Schraudolph.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Schraudolph

Reference 40

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.291284Z

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Observation feaa56e7-dcc1-4e55-bcbc-3660662e482e · outbound

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Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-05-14T19:32:52.708819Z

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Observation ee8beaa6-be5a-4d89-b866-aff692c5276e · outbound

This paper cites an unresolved cited work.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-05-14T19:32:52.713292Z

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Observation 6b1ab9d3-4c4d-4c76-8e32-e06e93dcff4c · outbound

This paper cites Fast estimation oftr(f(A)) via stochastic lanczos quadrature.SIAM Journal on Matrix Analysis and Applications, 38(4):1075–1099.

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions Fast estimation oftr(f(A)) via stochastic lanczos quadrature.SIAM Journal on Matrix Analysis and Applications, 38(4):1075–1099

Reference 43

Resolution: verified exact; doi, observed 2026-05-14T19:32:50.303157Z

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