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WORKSHOP - FAST DIRECT SOLVERS

Toulouse, June 24th-June 26th 2015

Programme and organization:
Click here 

Slides

Here is a partial list of the slides for talks given at the workshop:

Moody Chu

Eric Darve

Yuval Harness

Adrianna Gillman

Xiaoye Li

Gunnar Martinsson

Gregoire Pichon

Sergey Solovyev

Theo Mary

Clement Weisbecker


The purpose of this workshop is to address the following challenges in the design of efficient factorization algorithms for large sparse matrices: finding ways of reducing memory usage, operation counts, and data communication costs incurred during the factorization.
To this end, several low-rank approximation strategies have recently been proposed in the literature where conveniently defined off-diagonal blocks of a matrix are replaced by a more compact low-rank product. These techniques are particularly efficient when the original matrix is a discretization of some classes of partial differential equations, in which case the blocks are accurately and conveniently approximated by their low-rank representation.
Understanding the effect of the low-rank compression scheme on the overall backward error of the computed factors remains an open question. The derivation of a priori error bounds in terms of user-chosen parameters (such as the truncation levels, the norms of the blocks, and the block sizes) is still a largely unexplored research topic. On the other hand, the use of low-rank approximations leads to a workload whose weight is difficult to estimate, so that it is hard to schedule work in parallel. A careful workload distribution and the possibility of dynamically adjusting it, depending on how the computation proceeds, are potentially effective techniques to tackle this challenge. Modern parallel programming approaches based on the use of dynamic runtime engines may provide the tools needed to achieve the implementation of these complex methods on large scale, high performance platforms.

The workshop aims to gather experts in low-rank techniques as well as experts in numerical analysis and high performance computing and confront them with the abovementioned major challenges in the use of low-rank techniques within linear algebra – a topic whose popularity is becoming very widespread in the scientific computing community.

Interested participants are asked to propose a contribution to the workshop in the form of an abstract for a 30 minutes talk by December 31st 2014. Notifications of acceptance will be given by January 31st 2015.
For further details please contact Alfredo Buttari (alfredo.buttari@enseeiht.fr) or David Titley-Peloquin (titleypelo@cerfacs.fr).

 
 

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