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.
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
Miller, W.: On the Stability of Finite Numerical Methods. Numer. Math.19, 425–432 (1972).
Miller, W.: A Note on the Instability of Gaussian Elimination. BIT11, 422 424 (1971).
Miller, W., andR. Paulhamus: Automatic A Priori Round-off Analysis, Part II: Symbol Manipulation Conditions. Technical report, The Pennsylvania State University (1972).
Rudin, W.: Principles of Mathematical Analysis, 2nd ed. New York: McGraw-Hill. 1964.
Tarski, A.: A Decision Method for Elementary Algebra and Geometry. Berkeley, California: University of California Press. 1951.
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Our research was supported in part by NSF grant GJ-797.
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Miller, W. Automatic a priori round-off analysis. Computing 10, 97–106 (1972). https://doi.org/10.1007/BF02242384
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DOI: https://doi.org/10.1007/BF02242384