Greedy algorithms for high-dimensional non-symmetric linear problems

By É. Cancès, Virginie Ehrlacher, Tony Lelièvre. 2012

24 citations recorded by the source corpus.

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 considered 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.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Convergence results in this direction can be found in [3,39,40,84–86, A number of improvements to the simple scheme outlined above have been proposed to increase its convergence speed, see, e.g., [4, 95, 200, 202].”