Estimating the parallel performance of IQMR method for unsymmetric large and sparse linear systems
Bibliographic record
Abstract
For the solutions of linear systems of equations with unsymmetric coefficient matrices, we have proposed an improved version of the quasi-minimal residual (IQMR) method by using the Lanczos process as a major component combining elements of numerical stability and parallel algorithm design. The algorithm is derived such that all inner products and matrix-vector multiplications of a single iteration step are independent and communication time required for inner product can be overlapped efficiently with computation time. In this paper, we mainly present the qualitative analysis of the parallel performance with Store-and-Forward routing and Cut-Through routing schemes and topologies such as ring, mesh, hypercube and balanced binary tree. Theoretically it is shown that the hypercube topology can give us the best parallel performance with regards to parallel efficiency, speed-up, and runtime, respectively. We also study theoretical aspects of the overlapping effect in the algorithm. Some timing results are shown to verify the theoretical studies.
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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 | 0.001 | 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".