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Calculs et visualisation en nombres complexes

Abstract : The aim of this thesis is to provide some effective ways to compute and visualize mathematical objects arising in complex analysis. In this scope, many mathematical problems prevent from using complex numbers as naturally as real numbers : indeterminations occuring during computations, high number of dimensions obscuring naive visualization methods, many-valued phenomena. On the computing side, some methods has been studied, leading to the definition of a programming model enabling the detection and the resolution of indeterminations. On the visualization side, methods dealing with the visualization of complex functions have been applied to the visualization of complex Ordinary Differential Equations solutions. These methods have been implemented as modules in a common environment enabling rapid prototypings of experiments, caracterized by a strong coupling of visualization and computations. The different applications presented in this document (numerical integration of differential equations defined by many-valued functions, visualisation of solutions together with the global error estimated during integration) have been developped in this environment.
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Contributor : Thèses Imag <>
Submitted on : Friday, February 20, 2004 - 6:39:37 PM
Last modification on : Friday, November 6, 2020 - 4:09:37 AM
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  • HAL Id : tel-00004965, version 1



Laurent Testard. Calculs et visualisation en nombres complexes. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1997. Français. ⟨tel-00004965⟩



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