Formulation of Matrix Pade Approximation in Rectangular Full Packed Storage
Bibliographic record
Abstract
The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangularfull packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The proceduregiven by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequenceof lower triangular matrices of a matrix polynomial in Rectangular Full Packed format. This RFP format of a matrixpolynomial is applied to compute matrix Pade approximants of the matrix polynomial using Matrix Pade Extended EuclideanAlgorithm. Algorithms for the multiplication of two triangular matrices and inverse of a triangular matrix in RFPformat are also presented. The CPU time and memory comparison in computing the matrix Pade approximants of a matrixpolynomial between RFP format case and non packed case are elucidated in detail.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".