Krylov.jl: A Julia basket of hand-picked Krylov methods
Bibliographic record
Abstract
Krylov v0.10.2 Diff since v0.10.1 Merged pull requests: Reuse the buffer for LAPACK routines on CPU (#940) (@amontoison) implementation Line Search with Negative Curvature Detection with direction for CR (#985) (@farhadrclass) implementation Line Search with Negative Curvature Detection with direction for CG (#1008) (@farhadrclass) implementation Line Search with Negative Curvature Detection with direction for MINRES (#1011) (@farhadrclass) Update the unit tests on Mac (#1016) (@amontoison) Update the link for the reference of bicgstab(l) (#1017) (@amontoison) [documentation] Update the example for the Poisson equation with halo regions (#1018) (@amontoison) [documentation] Additional modification in custom_workspaces.md (#1019) (@amontoison) Update make.jl (#1020) (@amontoison) Remove all allocations in the in-place version of block-MINRES (#1022) (@amontoison) Update ksizeof for workspaces of block-Krylov solvers (#1023) (@amontoison) Minres qlp npc (#1026) (@farhadrclass) Closed issues: hermitian_lanczos and loss of orthogonality ? (#956) Is there a way to extract the Krylov Space? (#1007) Does Krylov use the S from LinearOperators? (#1009) How to Use Krylov.jl in Multithreading? (#1010) what is z in the docs? (#1012) GMRES using Float32 stagnates on Apple M2 (#1015)
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.382 | 0.298 |
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".