Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T12:47:23.996654Z
Paper Citation Record · LEDGER
A geodesic convexity-like structure for the polar decomposition of a square matrix
As of 16 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2412.13990.
A citation records a reference. It does not transfer a finding from one paper to another.
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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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Source: cited_works
Reference resolution
22 of 22 outbound references displayed
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- verified fuzzy18
- unresolved1
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- malformed identifier0
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b1a45141-9944-432d-b788-ddc6fee31196 · outbound
This paper cites Optimization algo- rithms on matrix manifolds.
A geodesic convexity-like structure for the polar decomposition of a square matrix Optimization algo- rithms on matrix manifolds
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.188298Z
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 02960bcf-a510-453b-a62f-04aaa8dc85e5 · outbound
This paper cites Generalized procrustes analysis and its ap plications in pho- togrammetry.
A geodesic convexity-like structure for the polar decomposition of a square matrix Generalized procrustes analysis and its ap plications in pho- togrammetry
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.181012Z
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 c448c792-1cc3-424d-a3e9-809fb68ed6d1 · outbound
This paper cites Characterization of optimization pro blems that are solv- able iteratively with linear convergence.
A geodesic convexity-like structure for the polar decomposition of a square matrix Characterization of optimization pro blems that are solv- able iteratively with linear convergence
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.173666Z
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 c35f7bb5-0eef-4e46-a592-bc9ff7fbad46 · outbound
This paper cites Geodesic convex ity of the sym- metric eigenvalue problem and convergence of steepest desc ent.
A geodesic convexity-like structure for the polar decomposition of a square matrix Geodesic convex ity of the sym- metric eigenvalue problem and convergence of steepest desc ent
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.165779Z
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 5fc89825-79e1-42e6-a18d-ef72f77f94b1 · outbound
This paper cites Optimality conditions on the orthogona l group.
A geodesic convexity-like structure for the polar decomposition of a square matrix Optimality conditions on the orthogona l group
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.157787Z
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 0318ec4c-685d-4c88-89a1-bab81146b091 · outbound
This paper cites A Note on Nesterov's Accelerated Method in Nonconvex Optimization: a Weak Estimate Sequence Approach.
A geodesic convexity-like structure for the polar decomposition of a square matrix A Note on Nesterov's Accelerated Method in Nonconvex Optimization: a Weak Estimate Sequence Approach
Reference 6
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- local_arxiv, observed 2026-08-11T12:47:24.042225Z
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 1b866fbf-8b0a-4fa1-b651-0e02f04c0abb · outbound
This paper cites A new scaling for newton’s ite ration for the polar decomposition and its backward stability.
A geodesic convexity-like structure for the polar decomposition of a square matrix A new scaling for newton’s ite ration for the polar decomposition and its backward stability
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.150623Z
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 9aafd785-fd26-4929-a5e1-af2fbd7a7dcd · outbound
This paper cites Error bounds, q uadratic growth, and linear convergence of proximal methods.
A geodesic convexity-like structure for the polar decomposition of a square matrix Error bounds, q uadratic growth, and linear convergence of proximal methods
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.143170Z
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 fe0c0231-2be1-4acc-bfa8-3f61897d3548 · outbound
This paper cites Studying Morphological Variation: Exploring the Shape Space in Evolutionary Anthropology.
A geodesic convexity-like structure for the polar decomposition of a square matrix Studying Morphological Variation: Exploring the Shape Space in Evolutionary Anthropology
Reference 9
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- verified exact
- local_arxiv, observed 2026-08-11T12:47:24.031955Z
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 ffc504c2-b70f-4839-89dc-0617982b4bcd · outbound
This paper cites On halley’s iteration method.
A geodesic convexity-like structure for the polar decomposition of a square matrix On halley’s iteration method
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.135743Z
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 aade470f-826f-4654-84d4-a39eb664d61a · outbound
This paper cites Accelerated Methods for $\alpha$-Weakly-Quasi-Convex Problems.
A geodesic convexity-like structure for the polar decomposition of a square matrix Accelerated Methods for $\alpha$-Weakly-Quasi-Convex Problems
Reference 11
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- verified exact
- local_arxiv, observed 2026-08-11T12:47:24.020859Z
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 648a9515-b5c8-44d0-bf4f-d1a55ed6d484 · outbound
This paper cites Gradient d escent learns linear dynamical systems.
A geodesic convexity-like structure for the polar decomposition of a square matrix Gradient d escent learns linear dynamical systems
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.128051Z
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 34275b6f-00bb-46fc-be40-4a5d33277292 · outbound
This paper cites Computing the polar decomposition—w ith applica- tions.
A geodesic convexity-like structure for the polar decomposition of a square matrix Computing the polar decomposition—w ith applica- tions
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.120484Z
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 d60f8d75-4839-4ebb-8408-7b964ed8673a · outbound
This paper cites Functions of matrices: Theory and co mputation, 2008.
A geodesic convexity-like structure for the polar decomposition of a square matrix Functions of matrices: Theory and co mputation, 2008
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.112973Z
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 4f989b37-002b-4074-84b1-13fbdf51982e · outbound
This paper cites A solution for the best rotation to rel ate two sets of vectors.
A geodesic convexity-like structure for the polar decomposition of a square matrix A solution for the best rotation to rel ate two sets of vectors
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.105044Z
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 19aac3e2-79f5-4ed5-b351-6cd3fad10506 · outbound
This paper cites Linear co nvergence of gradient and proximal-gradient methods under the polyak-ł ojasiewicz con- dition.
A geodesic convexity-like structure for the polar decomposition of a square matrix Linear co nvergence of gradient and proximal-gradient methods under the polyak-ł ojasiewicz con- dition
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.097747Z
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 df25e070-c6ee-4479-8911-273a1f1d7bff · outbound
This paper cites an unresolved cited work.
A geodesic convexity-like structure for the polar decomposition of a square matrix Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:47:24.089979Z
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 62ab2cc5-78c8-498f-b1c2-2c6d7bf3f728 · outbound
This paper cites Opti mizing halley’s iteration for computing the matrix polar decomposition.
A geodesic convexity-like structure for the polar decomposition of a square matrix Opti mizing halley’s iteration for computing the matrix polar decomposition
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.082238Z
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 eb3a5ae3-b580-4863-a35e-6ff277dab1ce · outbound
This paper cites Backward stabi lity of iterations for computing the polar decomposition.
A geodesic convexity-like structure for the polar decomposition of a square matrix Backward stabi lity of iterations for computing the polar decomposition
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.074291Z
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 ae105528-bdb6-4c60-bd2c-0242d35f1c97 · outbound
This paper cites Lin ear convergence of first order methods for non-strongly convex optimization.
A geodesic convexity-like structure for the polar decomposition of a square matrix Lin ear convergence of first order methods for non-strongly convex optimization
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.066299Z
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 23884369-e6b6-48e5-a0df-db7f55ea588f · outbound
This paper cites Introduction to Differential Geometry.
A geodesic convexity-like structure for the polar decomposition of a square matrix Introduction to Differential Geometry
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.058296Z
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 01c70155-8532-4d19-b438-e4759db0d57f · outbound
This paper cites A generalized solution of the ortho gonal procrustes problem.
A geodesic convexity-like structure for the polar decomposition of a square matrix A generalized solution of the ortho gonal procrustes problem
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:47:24.050612Z
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
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