Forward error analysis of Gaussian elimination. II: Stability theorems

DOI10.1007/BF01389493zbMath0554.65033OpenAlexW1507968835MaRDI QIDQ760169

Friedrich Stummel

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/133003

zbMATH Keywords

stabilitydeterminantgrowth factorsM-matricesstability estimatesband matricesa priori error and residualpivot elementssignregular

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Forward error analysis of Gaussian elimination. I: Error and residual estimates, Rounding errors in numerical solutions of two linear equations in two unknowns

Cites Work

• Forward error analysis of Gaussian elimination. I: Error and residual estimates
• Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler Länge
• On the LU factorization of M-matrices
• Backward error analysis for totally positive linear systems
• The LU-factorization of totally positive matrices
• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• Ein Kriterium für den Nachweis der Totalnichtnegativität von Bandmatrizen
• Perturbation Theory for Evaluation Algorithms of Arithmetic Expressions
• On the stability of Gauss-Jordan elimination with pivoting
• Rounding errors in numerical solutions of two linear equations in two unknowns
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