## Preliminary list of abstracts

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*Keywords:*Greedy algorithms, high-dimensional partial differential equations

- Infante Acevedo, José Arturo (CERMICS, Université Paris-Est, France)

We study an algorithm which has been proposed in [1,4] and analyzed in [2,3] to solve high dimensional partial differential equations. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum. This algorithm is very much related to so called greedy algorithms, see [5]. Convergence results of this approach obtained in [2,3] will be presented.

Besides, we will also show the application of this non linear
approximation method to the option pricing problem, an important
subject of the mathematical finance domain. This leads us to consider two
extensions of the standard algorithm, which applies to * symmetric linear*
partial differential equations: (i) * nonsymmetric linear* problems to value
European options, (ii) * nonlinear variational* problems to price American
options. We will present theoretical and numerical difficulties arising in
this context.

*J. Non-Newtonian Fluid Mech.*, 139:153–176, 2006.

*Constructive Approximation*, 30(3):621–651, 2009.

*Comput. Methods Appl. Mech. Engrg.*, 196:4521–4537, 2007.

*Acta Numerica*, 17:235–409, 2008.