Is a Computer a Perfect Computing Machine?

Jean-François COLONNA
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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Abstract: A computer is a programmable computing machine that is both finite and non continuous. Then most numbers and in particular the real numbers cannot be memorized and manipulated exactly. In most computations rounding-off errors will appear mostly in problems sensitive to initial conditions and these errors will propagate and amplify. The usual mathematical properties like associativity are lost and then two different computers regarding hardware and/or software running the same program could give different results.

Keywords: Nombres réels, Nombres Flottants, Erreurs d'arrondi, Associativité, Ordinateur, Real Numbers, Floating point numbers, Rounding-off errors, Associativity, Computer..

Copyright © Jean-François Colonna, 2010-2021.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2010-2021.