Paper Citation Record · LEDGER

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure

As of 20 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 1 inbound Pith citation observation for arXiv:2507.11724.

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

pith.paper-citation-record.v1
2507.11724 v1

Coverage vector

measured 62 of 62 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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

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Reference resolution

62 of 62 outbound references displayed

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External citation measurements

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Outbound references

Observation f0433b6a-ab8e-49b4-a832-9ee4539a0d0e · outbound

This paper cites Leverage score sampling for faster accelerated regression and erm.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Leverage score sampling for faster accelerated regression and erm

Reference 1

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Observation 95ecb02d-82f0-4e78-ad79-f4cdf3a9e198 · outbound

This paper cites Katyusha: The first direct acceleration of stochastic gradient methods.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Katyusha: The first direct acceleration of stochastic gradient methods

Reference 2

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Observation 4d5a5dfa-439b-457f-b5ac-ea1f8da0fe7f · outbound

This paper cites More asymmetry yields faster matrix multiplication.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure More asymmetry yields faster matrix multiplication

Reference 3

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Observation 9652fba1-4158-4b4b-9b1f-8e4cdfa15de9 · outbound

This paper cites Faster kernel ridge regression using sketching and preconditioning.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Faster kernel ridge regression using sketching and preconditioning

Reference 4

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Observation cb65c687-5726-4341-995e-c98fcb8a23ab · outbound

This paper cites On the rate of convergence of the preconditioned conjugate gradient method.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure On the rate of convergence of the preconditioned conjugate gradient method

Reference 5

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Observation 6b136cb3-a35d-49aa-a1d4-36a4f93e91de · outbound

This paper cites Optimal oblivious subspace embeddings with near-optimal sparsity.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Optimal oblivious subspace embeddings with near-optimal sparsity

Reference 6

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Observation 951fe63b-8c67-4fff-89f9-66c627af514f · outbound

This paper cites Optimal embedding dimension for sparse subspace embeddings.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Optimal embedding dimension for sparse subspace embeddings

Reference 7

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Observation 0a7cb02c-6600-463b-a857-9cb59312914d · outbound

This paper cites Clarkson and David P.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Clarkson and David P

Reference 8

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Observation 08edd9b0-a319-4ca0-97ec-c3b6bf73efef · outbound

This paper cites Nearly tight oblivious subspace embeddings by trace inequalities.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Nearly tight oblivious subspace embeddings by trace inequalities

Reference 9

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Observation bdb770af-c4ce-4fe9-b993-d8e1daed7622 · outbound

This paper cites Solving directed laplacian systems in nearly-linear time through sparse lu factorizations.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Solving directed laplacian systems in nearly-linear time through sparse lu factorizations

Reference 10

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Observation c943cbc6-d3af-47c6-9048-bdcbf64b4cff · outbound

This paper cites Cohen, Jonathan A.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Cohen, Jonathan A

Reference 11

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Observation 3babb9ee-464d-4d26-8c09-c6e8a4b7260e · outbound

This paper cites Cohen, Rasmus Kyng, Gary L.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Cohen, Rasmus Kyng, Gary L

Reference 12

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Observation 04c12a4c-42fc-4156-966c-4e4e4603a12f · outbound

This paper cites Cohen, Yin Tat Lee, Cameron Musco, Christopher Musco, Richard Peng, and Aaron Sidford.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Cohen, Yin Tat Lee, Cameron Musco, Christopher Musco, Richard Peng, and Aaron Sidford

Reference 13

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Observation 79f274e0-96f1-413b-81a0-b4e60902b536 · outbound

This paper cites Optimal approximate matrix product in terms of stable rank.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Optimal approximate matrix product in terms of stable rank

Reference 14

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Observation f389bd51-ae35-4784-9882-decd35dd6357 · outbound

This paper cites Matrix multiplication via arithmetic progressions.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Matrix multiplication via arithmetic progressions

Reference 15

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Observation 842ff77a-6f31-4ffc-9402-883ad0ae3413 · outbound

This paper cites Fast linear algebra is stable.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Fast linear algebra is stable

Reference 16

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Observation 824a91fb-0045-4514-a4f6-0802691dc222 · outbound

This paper cites Fine-grained Analysis and Faster Algorithms for Iteratively Solving Linear Systems.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Fine-grained Analysis and Faster Algorithms for Iteratively Solving Linear Systems

Reference 17

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This paper cites Faster linear systems and matrix norm approximation via multi-level sketched preconditioning.ACM-SIAM Symposium on Discrete Algorithms (SODA), 2025.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Faster linear systems and matrix norm approximation via multi-level sketched preconditioning.ACM-SIAM Symposium on Discrete Algorithms (SODA), 2025

Reference 18

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Observation 0253e6df-d79a-4172-b0a0-81aea3809f53 · outbound

This paper cites Randomized Kaczmarz Methods with Beyond-Krylov Convergence.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Randomized Kaczmarz Methods with Beyond-Krylov Convergence

Reference 19

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Observation 98f9c2b5-4aba-4fac-8ad2-61c10a617b0c · outbound

This paper cites Solving linear systems faster than via preconditioning.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Solving linear systems faster than via preconditioning

Reference 20

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This paper cites Randomized Nystr\"om Preconditioning.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Randomized Nystr\"om Preconditioning

Reference 21

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Observation 105a8e24-a6f7-4601-8130-87d044f4e5f2 · outbound

This paper cites Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimization.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimization

Reference 22

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Observation 8aac9b4c-3a70-47c7-b829-39e2ed7b7f09 · outbound

This paper cites Principal component projection without principal component analysis.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Principal component projection without principal component analysis

Reference 23

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This paper cites Faster eigenvector computation via shift-and-invert preconditioning.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Faster eigenvector computation via shift-and-invert preconditioning

Reference 24

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This paper cites Matrix computations.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Matrix computations

Reference 25

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Observation 36a69766-0b68-47a9-ac32-08ee7a04c24f · outbound

This paper cites Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order richardson iterative methods.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order richardson iterative methods

Reference 26

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Observation 79266890-e2bc-4654-af7b-d84553ff6d60 · outbound

This paper cites Solving ridge regression using sketched preconditioned svrg.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Solving ridge regression using sketched preconditioned svrg

Reference 27

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Observation 52a47818-61b7-4e29-b61f-d1b1730006f2 · outbound

This paper cites Behavior of slightly perturbed lanczos and conjugate-gradient recurrences.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Behavior of slightly perturbed lanczos and conjugate-gradient recurrences

Reference 28

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Observation 2fc8c636-502b-47a8-acfd-a552844de10f · outbound

This paper cites Methods of conjugate gradients for solving linear systems, volume 49.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Methods of conjugate gradients for solving linear systems, volume 49

Reference 29

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Observation 7a784a8b-2d8b-4ba6-a2e6-88d537b19224 · outbound

This paper cites Gaussian elimination.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Gaussian elimination

Reference 30

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Observation 593fd0b7-7453-4a90-899a-658a0558e6bf · outbound

This paper cites Structured semidefinite programming for recovering structured preconditioners.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Structured semidefinite programming for recovering structured preconditioners

Reference 31

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Observation 51155ddd-b9db-48ef-b806-9ac064107f7a · outbound

This paper cites Ultrasparse ultrasparsifiers and faster laplacian system solvers.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Ultrasparse ultrasparsifiers and faster laplacian system solvers

Reference 32

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Observation 9722e25b-aa4c-43ba-8910-57ee61b43627 · outbound

This paper cites Accelerating stochastic gradient descent using predictive variance reduc- tion.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Accelerating stochastic gradient descent using predictive variance reduc- tion

Reference 33

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Observation a96e8c41-c8a8-4aaf-98e4-a12f8fe8d02f · outbound

This paper cites Single pass spectral sparsification in dynamic streams.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Single pass spectral sparsification in dynamic streams

Reference 34

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Observation f4886cd3-4875-4356-bdba-c8e6c81281ac · outbound

This paper cites Miller, and Richard Peng.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Miller, and Richard Peng

Reference 35

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Observation 13d3ff89-7737-43c8-a75c-74dc558bb645 · outbound

This paper cites Miller, and Richard Peng.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Miller, and Richard Peng

Reference 36

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Observation 137c1f73-8156-4245-a20e-9b046798c64b · outbound

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

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Estimating the largest eigenvalue by the power and lanczos algorithms with a random start

Reference 37

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Observation 2567b221-bfac-44e6-abab-63ab424a0450 · outbound

This paper cites Sparsified cholesky and multigrid solvers for connection laplacians.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Sparsified cholesky and multigrid solvers for connection laplacians

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:16.343590Z

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Observation 07ec86cc-c84d-4273-b781-ee0933092059 · outbound

This paper cites Approximate gaussian elimination for laplacians-fast, sparse, and simple.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Approximate gaussian elimination for laplacians-fast, sparse, and simple

Reference 39

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Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Faster algorithms for rectangular matrix multiplication

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:16.268781Z

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Observation 3d327eb1-773e-4e1d-864f-92b89a962a98 · outbound

This paper cites Efficient accelerated coordinate descent methods and faster algorithms for solving linear systems.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Efficient accelerated coordinate descent methods and faster algorithms for solving linear systems

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:16.169771Z

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Observation 3195aa0d-c5a7-404d-ac63-e211aa61b7e1 · outbound

This paper cites Randomized methods for linear constraints: convergence rates and conditioning.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Randomized methods for linear constraints: convergence rates and conditioning

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:16.056494Z

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Observation 261ea882-66f7-48c3-9629-7f473443248c · outbound

This paper cites Miller, and Richard Peng.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Miller, and Richard Peng

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:15.951501Z

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Observation 549893fa-7b24-4991-aeab-fb5b757956dc · outbound

This paper cites A universal catalyst for first-order optimization.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure A universal catalyst for first-order optimization

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:15.853314Z

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Observation 6197efbe-74b2-4564-b368-a27f953498c1 · outbound

This paper cites Stability of the lanczos method for matrix function approximation.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Stability of the lanczos method for matrix function approximation

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:15.832308Z

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Observation 5f78be97-236f-4a15-9bc5-5559ff960d02 · outbound

This paper cites Spec- trum approximation beyond fast matrix multiplication: Algorithms and hardness.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Spec- trum approximation beyond fast matrix multiplication: Algorithms and hardness

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:15.558071Z

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Observation 9888734c-0138-41f1-85f6-ec9baceb40f5 · outbound

This paper cites Nguyˆ en.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Nguyˆ en

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:15.204990Z

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Observation 44064436-770d-4fbd-af3b-56d0ea4378c3 · outbound

This paper cites Nesterov.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Nesterov

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:14.786532Z

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Observation 87956472-9c75-451c-99f3-f1ca89ced0cb · outbound

This paper cites Nesterov and Sebastian U.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Nesterov and Sebastian U

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:14.610650Z

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Observation 57d74947-e8e2-418b-9612-d910515ef30a · outbound

This paper cites Algorithm Design Using Spectral Graph Theory.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Algorithm Design Using Spectral Graph Theory

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:14.602882Z

Source-reported events for the cited work

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Observation e3e7bb26-521d-46a0-abb7-2a798edc611c · outbound

This paper cites Sparsified block elimination for directed laplacians.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Sparsified block elimination for directed laplacians

Reference 51

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This paper cites A fast randomized algorithm for overdetermined linear least-squares regression.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure A fast randomized algorithm for overdetermined linear least-squares regression

Reference 52

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This paper cites Improved approximation algorithms for large matrices via random projections.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Improved approximation algorithms for large matrices via random projections

Reference 53

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This paper cites Spielman and Shang-Hua Teng.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Spielman and Shang-Hua Teng

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:14.118677Z

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This paper cites A Note on Preconditioning by Low-Stretch Spanning Trees.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure A Note on Preconditioning by Low-Stretch Spanning Trees

Reference 55

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This paper cites Gaussian elimination is not optimal.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Gaussian elimination is not optimal

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:14.014602Z

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This paper cites A randomized Kaczmarz algorithm with exponential conver- gence.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure A randomized Kaczmarz algorithm with exponential conver- gence

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:13.873479Z

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Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Unresolved cited work

Reference 58

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This paper cites Multiplying matrices faster than coppersmith-winograd.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Multiplying matrices faster than coppersmith-winograd

Reference 59

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This paper cites New bounds for matrix multiplication: from alpha to omega.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure New bounds for matrix multiplication: from alpha to omega

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:13.539211Z

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This paper cites Sketching as a tool for numerical linear algebra.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Sketching as a tool for numerical linear algebra

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:13.410680Z

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This paper cites Even faster accelerated coordinate descent using non-uniform sampling.

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure Even faster accelerated coordinate descent using non-uniform sampling

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:14:13.329587Z

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Pith citing papers

Observation 7a3216ad-bc63-4ab7-a83d-03ecab745535 · inbound

Faster Low-Rank Approximation and Kernel Ridge Regression via the Block-Nystr\"om Method cites this paper.

Faster Low-Rank Approximation and Kernel Ridge Regression via the Block-Nystr\"om Method Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure

Reference 12

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