Triple

T7833262
Position Surface form Disambiguated ID Type / Status
Subject Lyapunov equation E181625 entity
Predicate solvedBy P8791 FINISHED
Object Bartels–Stewart algorithm
The Bartels–Stewart algorithm is a numerical linear algebra method that efficiently solves certain matrix equations, particularly Sylvester and Lyapunov equations, using Schur decompositions.
 E695944 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Bartels–Stewart algorithm | Statement: [Lyapunov equation, solvedBy, Bartels–Stewart algorithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bartels–Stewart algorithm
Context triple: [Lyapunov equation, solvedBy, Bartels–Stewart algorithm]
  • A. Gaussian elimination
    Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
  • B. LinearAlgebra
    LinearAlgebra is Julia’s standard library module providing core functionality for vectors, matrices, and advanced linear algebra operations.
  • C. Jacobi method
    The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
  • D. Gauss–Seidel method
    The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
  • E. Schmidt orthogonalization
    Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Bartels–Stewart algorithm
Triple: [Lyapunov equation, solvedBy, Bartels–Stewart algorithm]
Generated description
The Bartels–Stewart algorithm is a numerical linear algebra method that efficiently solves certain matrix equations, particularly Sylvester and Lyapunov equations, using Schur decompositions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Bartels–Stewart algorithm
Target entity description: The Bartels–Stewart algorithm is a numerical linear algebra method that efficiently solves certain matrix equations, particularly Sylvester and Lyapunov equations, using Schur decompositions.
  • A. Gaussian elimination
    Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
  • B. LinearAlgebra
    LinearAlgebra is Julia’s standard library module providing core functionality for vectors, matrices, and advanced linear algebra operations.
  • C. Jacobi method
    The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
  • D. Gauss–Seidel method
    The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
  • E. Schmidt orthogonalization
    Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69ca8284a25c8190a1a20afad30da792 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb064a47648190af2ca2b336584a92 completed March 30, 2026, 11:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69cb5a9b7bb081909d6aa066ee064093 completed March 31, 2026, 5:24 a.m.
NEDg Description generation batch_69cb5ded0284819086c40a379b52a5bd completed March 31, 2026, 5:38 a.m.
NED2 Entity disambiguation (via description) batch_69cb765db28881909ac34071ec6889b3 completed March 31, 2026, 7:23 a.m.
Created at: March 30, 2026, 4:45 p.m.