Heterogeneous Tolerance Strategies in H-LU Decomposition for Integral Equations
Bibliographic record
Abstract
This research examines the use of heterogeneous tolerance strategies within the H -matrix framework to optimize solver performance for integral equations. The H-matrix method, widely employed in computational electromagnetics, is valued for reducing memory and computational complexity. A key aspect of this technique is managing block-wise accuracy, which can be adjusted across the matrix structure. This study introduces distinct tolerances for different block types in the block cluster tree. Specifically, leaf admissible blocks are assigned looser tolerances compared to non-leaf admissible blocks, reflecting their differing contributions to the solution process. Leaf blocks, often representing finer matrix levels, can operate with lower accuracy, while non-leaf blocks require higher precision to maintain overall solution accuracy. The research highlights the impact of these heterogeneous tolerances on solver efficiency. By allocating computational resources more effectively, the approach accelerates the solution process while preserving accuracy. A case study demonstrates the advantages of applying separate tolerances to leaf and non-leaf blocks, showcasing improved computational speed and solution precision.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".