Bibliographic record
Abstract
This chapter contains sections titled: Floating-Point Arithmetic The IEEE Standard Rounding Errors The Effects of Inexact Arithmetic: Some Illustrative Examples The Direct Solution of Linear Algebraic Systems Gaussian Elimination Back Substitution The LU Factorization Forward Elimination Scaling and Pivoting The Cholesky Factorization Banded and Sparse Matrices Rounding Errors, Condition Numbers, and Error Bounds Iterative Improvement The Iterative Solution of Linear Algebraic Systems Basic Iterative Methods The Conjugate-Gradient Method Overdetermined and Underdetermined Linear Systems The Normal Equations for Overdetermined Linear Systems The Normal Equations for Underdetermined Linear Systems Householder Transformations and the QR Factorization Using the QR Factorization to Solve Overdetermined Linear Systems Using the QR Factorization to Solve Underdetermined Linear Systems The Gram–Schmidt Orthogonalization Algorithm Using Gram–Schmidt to Solve Overdetermined Linear Systems Using Gram–Schmidt to Solve Underdetermined Linear Systems Eigenvalues and Eigenvectors of Matrices The Power Method The QR Method Transforming a Symmetric Matrix to Tridiagonal Form Inverse Iteration Other Methods Nonlinear Algebraic Equations and Systems Fixed-Point Iteration Newton's Method for Nonlinear Equations The Secant Method The Bisection and Regula Falsi Methods Convergence Rate of Convergence Newton's Method for Systems of Nonlinear Equations Modifications and Alternatives to Newton's Method Polynomial Equations Horner's Rule Unconstrained Optimization Some Definitions and Properties The Fibonacci and Golden-Section Search Methods The Steepest-Descent Method Conjugate-Direction Methods The Conjugate-Gradient Method Newton's Method Quasi-Newton Methods Approximation Polynomial Approximation Polynomial Interpolation Polynomial Interpolation with Derivative Data The Error in Polynomial Interpolation Piecewise Polynomials and Splines Piecewise Polynomial Interpolation Least-Squares Approximation Numerical Integration – Quadrature Simple Quadrature Rules Composite (Compound) Quadrature Rules Adaptive Quadrature Romberg Integration and Error Estimation Infinite Integrals and Singularities Monte-Carlo Methods Ordinary Differential Equations Initial-Value Problems (IVPs) Boundary-Value Problems (BVPs) Partial Differential Equations (PDEs) Classes of Problems and PDEs Classes of Numerical Methods for PDEs Finite-Difference Methods for BVPs Finite-Element Methods for BVPs Finite-Difference Methods for IVPs The Method of Lines Boundary-Element Methods The Multigrid Method Parallel Computation Cyclic Reduction Sources of numerical software
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.111 | 0.049 |
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".