Grégoire Pichon

Associate Professor, Université Claude Bernard Lyon 1

During my PhD thesis, I have integrated Block Low-Rank compression in the PaStiX solver, which solves sparse linear systems. The objective was to reduce both the time and the memory complexities by computing an approximate solution at a given accuracy. We have introduced low-rank compression and new dedicated kernels that perform low-rank addition for sparse structures, while maintaning the same level of parallelism than the original version of the PaStiX solver, to take advantage of all features that were developed in previous works. Low-rank compression integrated in sparse direct solvers may be impacted by the granularity of the block-data structure: blocks are generally small for sparse matrices. In order to reduce this burden, we have proposed a reordering strategy to reduce the number of off-diagonal blocks in the symbolic factorization. In addition, we have studied clustering strategies for increasing Block Low-Rank compressibility, which consist of special partitioning of separators that appear during the nested dissection. In the context of my Post-Doctorat, I was investigating the use of mixed precision floatting point operations for linear algebra. The objective is to compute some parts of an algorithm in a reduced precision, to minimize data movements and energy consumption. One of the main challenges is to control numerical properties of algorithms to maintain sufficient accuracy. I have been working on eigenproblems during an internship at Innovative Computing Laboratory (United States) and a visit at King Abdullah University of Science and Technology (Saudi Arabia). We have developed a task-based version of the Divide & Conquer algorithm to compute eigenpairs of symmetric tridiagonal matrices, as well as a task-based version of reduction of a dense matrix to a band matrix.