Application of the Arnoldi method in FDFD analysis of periodic guided-wave structure
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Bibliographic record
Abstract
This paper shows how to apply the Arnoldi method in accelerating the calculation of standard matrix eigenvalue problem with a highly sparse and structured matrix, which is formed when a finite difference frequency domain (FDFD) method is used to analyze the properties of periodic guided-wave structures. In most cases, the FDFD method for the analysis of periodic guided-wave structures will lead to a generalized nonsymmetrical sparse eigenvalue problem. A shift-and-invert Arnoldi method is applied for large nonsymmetrical generalized eigenvalue problems. The application of the Arnoldi technique makes the FDFD method more accurate, fast and practical.
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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 | 0.001 |
| 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) | 0.001 | 0.000 |
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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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