John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis

DOI10.1137/080734716zbMath1314.65005OpenAlexW1964962098MaRDI QIDQ3105795

Joseph F. Grcar

Publication date: 9 January 2012

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080734716

zbMATH Keywords

stabilityhistorycondition numberGaussian eliminationCFL conditionmatrix normsnumerical analysisvon Neumannbackward errorcomputer architecturecomputer arithmeticrounding error analysiscomputer programmingdecomposition paradigmstochastic linear algebra

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05) History of numerical analysis (65-03) History of computer science (68-03) Numerical algorithms for computer arithmetic, etc. (65Y04)

Related Items (8)

Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion PDEs ⋮ Rounding error analysis of linear recurrences using generating series ⋮ Mauro Picone, Sandro Faedo, and the numerical solution of partial differential equations in Italy (1928--1953) ⋮ Backward Error Analysis for Perturbation Methods ⋮ Strongly correlated random interacting processes. Abstracts from the workshop held January 28 -- February 3, 2018 ⋮ Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions ⋮ On the cost of iterative computations ⋮ Eigenvector correlations in the complex Ginibre ensemble

Uses Software

• mctoolbox
• Eigtool

This page was built for publication: John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis