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Record W4386248575 · doi:10.1017/9781009303897.007

Approximation

2023· book-chapter· en· W4386248575 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueCambridge University Press eBooks · 2023
Typebook-chapter
Languageen
FieldMathematics
TopicStatistical and numerical algorithms
Canadian institutionsUniversity of Guelph
Fundersnot available
KeywordsApplied mathematicsMathematicsPolynomial interpolationTrigonometric interpolationAlgorithmCalculus (dental)Mathematical analysisPolynomialLinear interpolation

Abstract

fetched live from OpenAlex

Chapter 6 starts out with a physics motivation, as well as a mathematical statement of the problems that will be tackled in later sections. First, polynomial interpolation is carried out using both the monomial basis and the Lagrange-interpolation formalism, sped up via the barycentric formula. This includes a derivation of the error and an emphasis on using unequally spaced points (Chebyshev nodes). Second, cubic-spline interpolation is introduced. Third, a section is dedicated to trigonometric interpolation, carefully working through the conventions and formalism needed to implement one of the most successful algorithms ever, the fast Fourier transform (FFT). Fourth, the topic of linear least-squares fitting is tackled, including the general formalism of the normal equations. The second edition includes a substantive new section on statistical inference, covering both frequentist and Bayesian approaches to linear regression. Nonlinear least-squares fitting is covered next, including the Gauss-Newton method and artificial neural networks. The chapter is rounded out by a physics project, on the experimental verification of the Stefan-Boltzmann law, and a problem set. In addition to providing a historical background on black-body radiation, the physics project shows an example of nonlinear least-squares fitting.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.896
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.068
GPT teacher head0.249
Teacher spread0.180 · 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