Geodesic
Greedy algorithms for high-dimensional non-symmetric linear problems
E. Cancès1 ; V. Ehrlacher1 ; T. Lelièvre1
1 Université Paris Est, CERMICS, projet MICMAC, Ecole des Ponts Paristech - INRIA, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France;
ESAIM. Proceedings, Tome 41 (2013), pp. 95-131.

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In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor product functions, each term of which is iteratively computed via a greedy algorithm ? . There exists a good theoretical framework for these methods in the case of (linear and nonlinear) symmetric elliptic problems. However, the convergence results are not valid any more as soon as the problems under consideration are not symmetric. We present here a review of the main algorithms proposed in the literature to circumvent this difficulty, together with some new approaches. The theoretical convergence results and the practical implementation of these algorithms are discussed. Their behaviors are illustrated through some numerical examples.
DOI : 10.1051/proc/201341005

E. Cancès 1 ; V. Ehrlacher 1 ; T. Lelièvre 1

1 Université Paris Est, CERMICS, projet MICMAC, Ecole des Ponts Paristech - INRIA, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France; 
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     title = {Greedy algorithms for high-dimensional non-symmetric linear problems},
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E. Cancès; V. Ehrlacher; T. Lelièvre. Greedy algorithms for high-dimensional non-symmetric linear problems. ESAIM. Proceedings, Tome 41 (2013), pp. 95-131. doi : 10.1051/proc/201341005. http://geodesic.mathdoc.fr/articles/10.1051/proc/201341005/

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