A dynamical strategy for approximation methods

Fabienne Jézéquel 1
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : The numerical result provided by an approximation method is affected by a global error, which consists of both a truncation error and a round-off error. Let us consider the converging sequence generated by successively dividing by two the step size used. If computations are performed until, in the convergence zone, the difference between two successive approximations is only due to round-off errors, then the global error on the result obtained is minimal. Furthermore its significant bits which are not affected by round-off errors are in common with the exact result, up to one.
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Submitted on : Tuesday, April 28, 2015 - 2:42:45 PM
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Fabienne Jézéquel. A dynamical strategy for approximation methods. Comptes Rendus Mécanique, Elsevier Masson, 2006, 334 (6), pp.362-367. ⟨10.1016/j.crme.2006.04.005⟩. ⟨hal-01146491⟩

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