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Record W1612003494 · doi:10.48550/arxiv.1105.1185

Iterative Methods for Computing Eigenvalues and Eigenvectors

2011· preprint· en· W1612003494 on OpenAlexaff
Maysum Panju

Bibliographic record

VenuearXiv (Cornell University) · 2011
Typepreprint
Languageen
FieldComputer Science
TopicMatrix Theory and Algorithms
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsPower iterationRayleigh quotient iterationEigenvalues and eigenvectorsInverse iterationIterative methodMathematicsMatrix-free methodsApplied mathematicsLinear algebraEigenvalues and eigenvectors of the second derivativeModal matrixPolynomialEigenvalue perturbationEigenvalue algorithmMatrix (chemical analysis)AlgorithmSymmetric matrixDiagonalizable matrixMathematical analysisSparse matrixSquare matrixGeometry

Abstract

fetched live from OpenAlex

We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The derivations, procedure, and advantages of each method are briefly discussed.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.004
metaresearch head score (Gemma)0.018
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.005
Threshold uncertainty score0.021

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0040.018
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.002
Science and technology studies0.0010.002
Scholarly communication0.0010.002
Open science0.0020.002
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0050.003

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.109
GPT teacher head0.255
Teacher spread0.146 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreMethods

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations56
Published2011
Admission routes1
Has abstractyes

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