Perturbation Theory for Evaluation Algorithms of Arithmetic Expressions

DOI10.2307/2007438zbMath0515.65039OpenAlexW4236317852MaRDI QIDQ3662526

Friedrich Stummel

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/2007438

zbMATH Keywords

error propagationcondition numbersbackward analysisrounding error analysisevaluation algorithmsforward analysislinear error equationsa priori and a posteriori error estimates

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

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Cites Work

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• Errata: “Efficient Calculation of the Effects of Roundoff Errors”
• Software for Roundoff Analysis
• Taylor expansion of the accumulated rounding error
• Computational Graphs and Rounding Error
• Computer Search for Numerical Instability
• Software for roundoff analysis, II
• Rounding errors in numerical solutions of two linear equations in two unknowns
• A Theory of Condition
• Zusammenfassender Bericht. Genauigkeitsfragen bei der Lösung linearer Gleichungssysteme
• On some topological properties of numerical algorithms
• Numerical Stability in Problems of Linear Algebra