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Convergence et applications d'approximations rationnelles vectorielles

Abstract : The Padé approximants and their generalizations are for many years the matter of intense researchs .Yet , many theoritical problems stay in suspense : problems of exitence and unicity , problems of convergence and acceleration of convergence .The purpose of the present work vas to give answers to such questions .In the first section we take an in terest in vector Padé approximants of matrix series .Conditions of existence and unicity ,results of convergence are given ,as also the link with the theory of Lanczos method for the resolution of linear Systems . We utilize also the vector Padé approximants to provide a simultaneous approximation of a function and its derivative .In the second section a sufficient condition for the quadratic convergence of the topological epsilon algorithm for Systems of nonlinear equations is given . Results of acceleration of convergence are proved for the second column of the vector epsilon algorithm , and more generaly for vector quasi linear trasformations .The third section deals with some Padé type approximants of entiere functions.In the last section a link between biorthogonality ,Gram - Schmidt process , linear System and interpolation is made .
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Contributor : Hervé Le Ferrand <>
Submitted on : Tuesday, September 28, 2010 - 1:10:54 PM
Last modification on : Saturday, December 19, 2020 - 3:03:38 AM
Long-term archiving on: : Friday, December 2, 2016 - 8:55:32 AM


  • HAL Id : tel-00521678, version 1


Hervé Le Ferrand. Convergence et applications d'approximations rationnelles vectorielles. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 1992. Français. ⟨tel-00521678⟩



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