Paper Citation Record · LEDGER

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures

As of 4 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2509.11152.

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

pith.paper-citation-record.v1
2509.11152 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T17:06:14.009425Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-25T07:04:23.292976Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-25T07:05:26.544428Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy0
unresolved27
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 701e559f-bec6-4e55-b586-5a54288bf24b · outbound

This paper cites an unresolved cited work.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.946371Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 847d64b7-f58e-49e4-942d-df0e5e96957f · outbound

This paper cites Fast direct methods for Gaussian processes.IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(2):252–265, 2015.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Fast direct methods for Gaussian processes.IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(2):252–265, 2015

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.949839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2239a5ef-e81d-428a-89ad-5861ac0b790f · outbound

This paper cites Existence ofH-matrix approximants to the inverse FE-matrix of elliptic operators withL ∞-coefficients.Numerische Mathematik, 95:1–28, 2003.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Existence ofH-matrix approximants to the inverse FE-matrix of elliptic operators withL ∞-coefficients.Numerische Mathematik, 95:1–28, 2003

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.952489Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e4ab3c0-43c9-4e65-a038-04ca1706c9b9 · outbound

This paper cites Approximating Gaussian processes withH 2-matrices.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Approximating Gaussian processes withH 2-matrices

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.955178Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0bb6681-a321-4b22-a469-b008803a3147 · outbound

This paper cites Introduction to hierarchical matrices with applications.Engineering analysis with boundary elements, 27(5):405–422, 2003.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Introduction to hierarchical matrices with applications.Engineering analysis with boundary elements, 27(5):405–422, 2003

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.957829Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7b3d312-dc07-4692-89e5-2e93e8389d9b · outbound

This paper cites Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates.Computing and Visualization in Science, 16:247–258, 2013.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates.Computing and Visualization in Science, 16:247–258, 2013

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.960640Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4428774e-c057-4fdd-96fc-e844e154fd3d · outbound

This paper cites Adaptive Sketching Based Construction of H2 Matrices on GPUs.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Adaptive Sketching Based Construction of H2 Matrices on GPUs

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.963411Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a2a52fe-39f6-4896-9d6a-9f8c9be31791 · outbound

This paper cites Hierarchical matrix operations on GPUs: Matrix-vector multiplication and compression.ACM Transactions on Mathematical Software, 45(1):1–28, February 2019.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Hierarchical matrix operations on GPUs: Matrix-vector multiplication and compression.ACM Transactions on Mathematical Software, 45(1):1–28, February 2019

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.965619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da54afaa-3700-44ff-87c6-95a7b172d9c2 · outbound

This paper cites A fast solver for HSS representations via sparse matrices.SIAM Journal on Matrix Analysis and Applications, 29(1):67–81, 2007.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A fast solver for HSS representations via sparse matrices.SIAM Journal on Matrix Analysis and Applications, 29(1):67–81, 2007

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.967868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72fceacb-95d3-4502-9574-c118b81bc102 · outbound

This paper cites A superfast algorithm for Toeplitz systems of linear equations.SIAM Journal on Matrix Analysis and Applications, 29(4):1247–1266, 2008.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A superfast algorithm for Toeplitz systems of linear equations.SIAM Journal on Matrix Analysis and Applications, 29(4):1247–1266, 2008

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.970201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3fc1a00b-f2ac-4745-abbe-04ec490ca844 · outbound

This paper cites Scalable and memory- efficient kernel ridge regression.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Scalable and memory- efficient kernel ridge regression

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.972493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99bfb7af-4267-4089-8162-579e6029b4ee · outbound

This paper cites The inverse fast multipole method: using a fast approximate direct solver as a preconditioner for dense linear systems.SIAM Journal on Scientific Computing, 39(3):A761– A796, 2017.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures The inverse fast multipole method: using a fast approximate direct solver as a preconditioner for dense linear systems.SIAM Journal on Scientific Computing, 39(3):A761– A796, 2017

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.974738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab49000a-bedb-4fe1-9aa9-8f48adfc65fd · outbound

This paper cites A robust parallel preconditioner for indefinite systems using hierarchical matrices and randomized sampling.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A robust parallel preconditioner for indefinite systems using hierarchical matrices and randomized sampling

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.977092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c13352b-4702-4675-a940-a8100198b561 · outbound

This paper cites A direct solver withO(N)complexity for integral equations on one-dimensional domains.Frontiers of Mathematics in China, 7:217–247, 2012.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A direct solver withO(N)complexity for integral equations on one-dimensional domains.Frontiers of Mathematics in China, 7:217–247, 2012

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.979459Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7fd9f07-30d4-41ff-81f4-dd22b4fa2d36 · outbound

This paper cites A sparse matrix arithmetic based onH-matrices.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A sparse matrix arithmetic based onH-matrices

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.981640Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 184b37cf-f457-4317-b48c-bd98e8febc5b · outbound

This paper cites Hierarchical algorithms on hierarchical architectures.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Hierarchical algorithms on hierarchical architectures

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.983976Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22082030-8024-41d8-8368-d4a7517276c8 · outbound

This paper cites Ho and Lexing Ying.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Ho and Lexing Ying

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.986947Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fe6dea8-e605-4b0d-8d06-214ca27cb113 · outbound

This paper cites AnO(N)distributed-memory parallel direct solver for planar integral equations.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures AnO(N)distributed-memory parallel direct solver for planar integral equations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.989210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30fd123b-9b2a-4837-a01d-c5dbefd9aeb9 · outbound

This paper cites an unresolved cited work.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.991453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fafe1ef8-0e80-46c5-b01d-d61025c79df8 · outbound

This paper cites Scalable linear time dense direct solver for 3-d problems without trailing sub-matrix dependencies.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Scalable linear time dense direct solver for 3-d problems without trailing sub-matrix dependencies

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.993681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d632ff18-7bff-491e-90d4-5c51daf0c5bd · outbound

This paper cites an unresolved cited work.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.995984Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a1d6dfe-e735-4c7e-9633-9937c4f5388c · outbound

This paper cites A fast direct solver for boundary integral equations in two dimensions.Journal of Computational Physics, 205(1):1–23, 2005.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A fast direct solver for boundary integral equations in two dimensions.Journal of Computational Physics, 205(1):1–23, 2005

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:13.998282Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0469190-a0fc-485e-855f-6976b308108c · outbound

This paper cites A recursive skeletonization factorization based on strong admissibility.Multiscale Modeling & Simulation, 15(2):768–796, 2017.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures A recursive skeletonization factorization based on strong admissibility.Multiscale Modeling & Simulation, 15(2):768–796, 2017

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:14.000507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7f16c6b-781b-43dc-8e6d-591f5ab33e52 · outbound

This paper cites FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions.Multiscale Modeling & Simulation, 21(4):1570–1601, 2023.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions.Multiscale Modeling & Simulation, 21(4):1570–1601, 2023

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:14.002718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c73eae95-707f-4804-92a6-fbbc7ff2702e · outbound

This paper cites Randomized sparse direct solvers.SIAM Journal on Matrix Analysis and Applications, 34(1):197– 227, 2013.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Randomized sparse direct solvers.SIAM Journal on Matrix Analysis and Applications, 34(1):197– 227, 2013

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:14.004868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af9e09f3-bb5c-4d14-ab98-1f417b24d825 · outbound

This paper cites Randomized Strong Recursive Skeletonization: Simultaneous Compression and LU Factorization of Hierarchical Matrices using Matrix-Vector Products, 2025.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures Randomized Strong Recursive Skeletonization: Simultaneous Compression and LU Factorization of Hierarchical Matrices using Matrix-Vector Products, 2025

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:14.007080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52afd4b8-8e2f-4ee0-9ed7-4fc8f197e8a0 · outbound

This paper cites H2Opus: a distributed- memory multi-GPU software package for non-local operators.Advances in Computational Mathematics, 48(3), May 2022.

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures H2Opus: a distributed- memory multi-GPU software package for non-local operators.Advances in Computational Mathematics, 48(3), May 2022

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T17:06:14.009425Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 8a2c0f8e-f9b6-4375-8f4f-49b81d7dc50b · inbound

Parallel Sparse and Data-Sparse Factorization-based Linear Solvers cites this paper.

Parallel Sparse and Data-Sparse Factorization-based Linear Solvers Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-25T07:05:26.546704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.