A comparative study of wavelet matrix transformations for the solution of integral equations
Bibliographic record
Abstract
The application of wavelets for the solution of electromagnetic field integral equation yields sparse matrix equations which can be solved efficiently by using sparse matrix techniques. In this paper, the wavelet matrix transforms using the semi-orthogonal wavelets (SOW) and the Daubechies orthogonal wavelets (DOW) are applied to the solution of integral equations and their performance is compared by investigating the convergence rate when the conjugate gradient (CG) method is employed. Since the SOW transform yields a matrix with a larger condition number than that corresponding to the DOW transform, it is expected that the convergence rate is much better in the latter case. Numerical simulations are conducted for the transverse magnetic (TM) scattering by conducting cylinders and the convergence rate of the CG iterative process is determined for the matrix equations transformed using the SOW and the DOW. The computed results confirm the theoretical expectations.
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How this classification was reachedexpand
Full frame distilled prediction
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)
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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".