Imprécisions numériques : méthode d'estimation et de contrôle de la précision en C.A.O

Abstract : The object of this thesis is to bring a solution of numerical problems caused by the use of floating point arithmetic. The first chapter tackles the problems which are induced by the floating point arithmetic. One also develop the different existing methods and tools to solve these problems. The second chapter is devoted to the study of the spreader of errors during algorithms. Differential analysis is not adequate to obtain a good approximation of errors affecting the results of calculation. We next determine an estimation of the loss of precision during the calculation of the intersection point of two lines, according to the angle they draw up. The third chapter presents the method CESTAC (Stochastic checking of rounding of calculaation) [vig 93] which allows to estimate the number of significant digits affecting the result of a numerical calculation. The fourth chapter deals with computer algebra, as with the rational arithmetic and specially with the utilization of software Pari in order to avoid the problems caused by large integers. The fifth chapter describes our methodology which consists to determine the precision of a calculation with the assistance of the method CESTAC and which, if the precision isn't sufficient, uses the rational arithmetic. We also amend the conditional instructions, so that the tests be executed according to the precision of each data
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Denise Pirus. Imprécisions numériques : méthode d'estimation et de contrôle de la précision en C.A.O. Autre [cs.OH]. Université Paul Verlaine - Metz, 1997. Français. ⟨NNT : 1997METZ003S⟩. ⟨tel-01777191⟩

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