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Dualité algébrique, structures et applications.

Olivier Ruatta 
Abstract : In this thesis we are interested in quotient algebra structures and more specifically in contributions of duality theory to representation theory of coordinate algebras of zero-dimensional algebraic sets. The first part of the text is dedicated to representation theory of zero dimensional algebras and to interpolation problems. We generalize Lagrange and Hermite interpolation bases and give explicit formulae for them. In this framework we give closed formulae linking the roots of an algebraic system and its coefficients. In a second part, we apply those results to the design of iterative methods for simultaneous approximation of all roots of algebraic systems. The third part is dedicated to algebraic residues, their computational aspects and applications. In the last part, we are interested in algorithms linked to quasi-Toeplitz, quasi-Hankel, \ldots matrices as defined by B. Mourrain and V.Y. Pan. We show applications of such algorithms to asymptotic accelerations of iterative methods to solve algebraic systems.
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Contributor : Olivier Ruatta Connect in order to contact the contributor
Submitted on : Wednesday, January 8, 2003 - 1:46:14 PM
Last modification on : Monday, March 21, 2016 - 5:49:26 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 7:15:19 PM


  • HAL Id : tel-00002243, version 1



Olivier Ruatta. Dualité algébrique, structures et applications.. Modélisation et simulation. Université de la Méditerranée - Aix-Marseille II, 2002. Français. ⟨tel-00002243⟩



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