Computing

, Volume 10, Issue 1–2, pp 97–106 | Cite as

Automatic a priori round-off analysis

Part I: Arithmetic Conditions
  • W. Miller
Article

Abstract

The effect of rounding errors on an algebraic process is often investigated by means of a so-called backward analysis. In this paper we will discuss the possibility of performing such an analysis on a computer. We begin with a precise definition of a stable algorithm, i.e., an algorithm which is relatively insensitive to rounding errors.

Keywords

Computational Mathematic Precise Definition Stable Algorithm Algebraic Process 

Automatische A-priori-Rundungsanalyse, I

Zusammenfassung

Der Effekt der Rundungsfehler in einem algebraischen Prozeß wird oft mit einer sogenannten Rückwärtsanalyse untersucht. Wir wollen hier die Möglichkeit untersuchen, diese Analyse auf einem Computer auszuführen. Wir beginnen mit einer genauen Definition eines stabilen Algorithmus, oder aber eines Algorithmus der relativ unempfindlich auf Rundungsfehler reagiert.

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References

  1. [1]
    Miller, W.: On the Stability of Finite Numerical Methods. Numer. Math.19, 425–432 (1972).CrossRefGoogle Scholar
  2. [2]
    Miller, W.: A Note on the Instability of Gaussian Elimination. BIT11, 422 424 (1971).CrossRefGoogle Scholar
  3. [3]
    Miller, W., andR. Paulhamus: Automatic A Priori Round-off Analysis, Part II: Symbol Manipulation Conditions. Technical report, The Pennsylvania State University (1972).Google Scholar
  4. [4]
    Rudin, W.: Principles of Mathematical Analysis, 2nd ed. New York: McGraw-Hill. 1964.Google Scholar
  5. [5]
    Tarski, A.: A Decision Method for Elementary Algebra and Geometry. Berkeley, California: University of California Press. 1951.Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • W. Miller
    • 1
  1. 1.Computer Science DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

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