A New Splitting Technique for Solving Nonlinear Equations by an Iterative Scheme
Why this work is in the frame
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Bibliographic record
Abstract
Using a new trick, the nonlinear equation is recast to a coupled system consisting of a linear equation and a nonlinear equation. For the latter, with a weight factor we split the nonlinear term into two parts on both sides of the equation. When the two-dimensional nonlinear system is linearized around the iteration point to be a linear system, we can easily solve it and develop a fast convergent iterative scheme to solve nonlinear equations. In order to further enhance the convergence speed, a linear term is added on both sides of the first linear equation, which results to a very powerful iterative scheme with parameter being analyzed by the eigenvalues. The new iterative scheme is proved to be absolutely convergent, and the number of iterations for convergence is estimated. The merits of the present iterative scheme are insensitive to the initial guess of the solution, convergent very fast, and without needing of the differentials of the function.
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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 | 0.008 | 0.027 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it