Abstract
Methods are presented for performing various error analyses of numerical algorithms. These analyses include forward, backward, and B-analysis (a combination of forward and backward). These analyses additionally provide alternative criteria by which different algorithms that solve the same problem may be compared. The conclusions of various comparison criteria are related to the correlation of errors in each algorithm. Finally, the analysis of a composite algorithm, which is made up of concatenated sub-algorithms, is given in terms of analyses done on its parts.
Zusammenfassung
In dieser Arbeit werden Methoden vorgestellt, die es gestatten, verschiedene Fehleranalysen numerischer Algorithmen zu vollziehen. Darunter befinden sich Vorwärts- und Rückwärtsanalyse (forward and backward analysis) sowie beidseitige Analyse (B-analysis, eine Kombination von forward and backward) ein. Diese Analysen liefern zusätzlich weitere Kriterien, durch welche verschiedene Algorithmen, die dasselbe Problem lösen, verglichen werden können. Die Aussagen der verschiedenen Vergleichskriterien beziehen sich auf die Fehlerkorelation in jedem Algorithmus. Schließlich wird die Analyse zusammengesetzter Algorithmen, welche aus verketteten Subalgorithmen bestehen, mit Hilfe der Analysen, die an den Teilen vollzogen wurden, dargestellt.
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Abbreviations
- 5.10:
-
General
- 5. 11:
-
Error Analysis
- 5. 14:
-
Linear Algebra
- 5. 41:
-
Linear Programming
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This work was supported in part by the National Science Foundation under NSF Grant MCS 75-21758.
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Larson, J.L., Sameh, A.H. Algorithms for roundoff error analysis —A relative error approach. Computing 24, 275–297 (1980). https://doi.org/10.1007/BF02237815
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DOI: https://doi.org/10.1007/BF02237815