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Record W4232786831 · doi:10.1002/3527607773.ch10

Numerical Methods

2005· other· en· W4232786831 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

Venuenot available
Typeother
Languageen
FieldComputer Science
TopicMatrix Theory and Algorithms
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsOverdetermined systemMathematicsConjugate gradient methodUnderdetermined systemSystem of linear equationsQR decompositionApplied mathematicsCholesky decompositionPreconditionerPolynomialIterative methodEigenvalues and eigenvectorsMathematical analysisAlgorithm

Abstract

fetched live from OpenAlex

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

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: none
Teacher disagreement score0.617
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0180.002

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.

Opus teacher head0.014
GPT teacher head0.325
Teacher spread0.311 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Quick stats

Citations4
Published2005
Admission routes1
Has abstractyes

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