jeudi 18 mars 2010 , 14h30
Intervenant : Hassane SADOK (LMPA)
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Titre :  Extrapolation vectorielle et applications.
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Résumé:
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The convergence of iterates determined by a slowly convergent
iterative process often can be accelerated by extrapolation
methods. In this talk we will give a survey of vector
extrapolation methods such as the reduced rank extrapolation (RRE) 
of Eddy and Mesina, the minimal polynomial extrapolation (MPE)
of Cabay and Jackson, the modified minimal polynomial
extrapolation (MMPE) of Brezinski and Pugachev and the 
topological epsilon-algorithm (TEA) of Brezinski.
Using projectors, we derive a different interpretation of these
methods and give some theoretical results. The second part of 
this talk is devoted to some numerical applications of the
vector extrapolationmethods to some problems involving linear,
nonlinear systems of equations obtained from finite-difference
or finite-element discretization of continuum problems.
The truncated singular value decomposition (TSVD) is a popular
solution method for small to moderately sized linear ill-posed
problems. The truncation index can be thought of as a 
regularization parameter; its value affects the quality of 
the computed approximate solution. The choice of a suitable
 value of the truncation index generally is important, but 
can be difficult without auxiliary information about the 
problem being solved.
We will describes how vector extrapolation methods can be 
combined with TSVD, and illustrates that the determination 
of the proper value of the truncation index is less critical 
for the combined extrapolation-TSVD method than for TSVD alone.