Forward error analysis of Gaussian elimination. I: Error and residual estimates

DOI10.1007/BF01389492zbMath0554.65032OpenAlexW3001742371MaRDI QIDQ760168

Friedrich Stummel

Publication date: 1985

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133002

zbMATH Keywords

numerical examplescancellationGaussian eliminationsuperpositionlinearization methodcondition numbersrounding errorsbackward error analysisforward error analysisdata perturbationsarithmetic floating-point operationsoptimal componentwise error and residual estimatesresidual stability constantsscaling-invariant

Mathematics Subject Classification ID

Roundoff error (65G50) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (3)

The forward rounding error analysis of the partial pivoting quaternion LU decomposition ⋮ Forward error analysis of Gaussian elimination. II: Stability theorems ⋮ Strict optimal a posteriori error and residual bounds for Gaussian elimination in floating-point arithmetic

Cites Work

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• Forward error analysis of Gaussian elimination. II: Stability theorems
• Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler Länge
• Perturbation Theory for Evaluation Algorithms of Arithmetic Expressions
• Error Analysis of Direct Methods of Matrix Inversion
• Rounding errors in numerical solutions of two linear equations in two unknowns

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