Sparse matrix computations with application to solve system of nonlinear equations
Bibliographic record
Abstract
Numerical linear algebra is an essential ingredient in algorithms for solving problems in optimization, nonlinear equations, and differential equations. Spanning diverse application areas, from economic planning to complex network analysis, modeling and solving problems arising in those areas share a common theme: numerical calculations on matrices that are sparse or structured or both. Linear algebraic calculations involving sparse matrices of order 109 are now routine. In this article, we give an overview of scientific calculations where effective utilization of properties such as sparsity, problem structure, etc. play a vital role and where the linear algebraic calculations are much more complex than their dense counterpart. This is partly because operation and storage involving known zeros must be avoided, and partly because the fact that modern computing hardware may not be amenable to the specialized techniques needed for sparse problems. We focus on sparse calculations arising in nonlinear equation solving using the Newton method. This article is categorized under: Applications of Computational Statistics > Computational Mathematics Data: Types and Structure > Categorical Data Algorithms and Computational Methods > Quadratic and Nonlinear Programming Algorithms and Computational Methods > Numerical Methods
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".