Optimal minimax algorithm for integrating fast oscillatory functions in two dimensions
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Bibliographic record
Abstract
In this paper, we give a complete description of efficient formulae for the numerical integration of fast oscillating functions of two variables. The focus is on the case encountered frequently in many engineering applications where an accurate value of the Lipschitz constant is not available. Using spline approximations, we demonstrate the main idea of our approach on the example of piecewise bilinear interpolation, and propose optimal‐by‐order (with a constant not exceeding two) cubature formulae that are applicable for a wide range of oscillatory patterns. This property makes the formulae indispensable in many engineering applications dealing with signal processing and image recognition. Illustrative results of numerical experiments are presented.
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Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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