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- Patrick Amestoy, Iain S. Duff, Jean-Yves L'Excellent, Yves Robert, François-Henry Rouet, Bora Uçar
- SIAM J. Scientific Computing
- 2012

The inverse of an irreducible sparse matrix is structurally full, so that it is impractical to think of computing or storing it. However, there are several applications where a subset of the entries of the inverse is required. Given a factorization of the sparse matrix held in out-of-core storage, we show how to compute such a subset efficiently, by… (More)

- François-Henry Rouet, Xiaoye S. Li, Pieter Ghysels, Artem Napov
- ACM Trans. Math. Softw.
- 2016

In this report, we replicate a subset of the performance results in the article “A distributed-memory package for dense Hierarchically Semi-Separable matrix computations using randomization.”

- Pieter Ghysels, Xiaoye S. Li, François-Henry Rouet, Samuel Williams, Artem Napov
- SIAM J. Scientific Computing
- 2016

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized… (More)

We consider the solution of very large sparse systems of linear equations on parallel architectures. In this context, memory is often a bottleneck that prevents or limits the use of direct solvers, especially those based on the multifrontal method. This work focuses on memory and performance issues of the two memory and computationally intensive phases of… (More)

- Patrick Amestoy, Iain S. Duff, Jean-Yves L'Excellent, François-Henry Rouet
- SIAM J. Scientific Computing
- 2015

In this paper, we are concerned about computing in parallel several entries of the inverse of a large sparse matrix. We assume that the matrix has already been factorized by a direct method and that the factors are distributed. Entries are efficiently computed by exploiting sparsity of the right-hand sides and the solution vectors in the triangular solution… (More)

- Shen Wang, Xiaoye S. Li, François-Henry Rouet, Jianlin Xia, Maarten V. de Hoop
- ACM Trans. Math. Softw.
- 2016

We present a structured parallel geometry-based multifrontal sparse solver using hierarchically semiseparable (HSS) representations and exploiting the inherent low-rank structures. Parallel strategies for nested dissection ordering (taking low rankness into account), symbolic factorization, and structured numerical factorization are shown. In particular, we… (More)

- Emmanuel Agullo, Patrick R. Amestoy, Alfredo Buttari, Abdou Guermouche, Jean-Yves L'Excellent, François-Henry Rouet
- SIAM J. Scientific Computing
- 2016

We focus on memory scalability issues in multifrontal solvers like MUMPS. We illustrate why commonly used mapping strategies (e.g., a proportional mapping) cannot achieve a high memory efficiency. We propose a class of “memory-aware” algorithms that aim at maximizing performance under memory constraints. These algorithms provide both accurate memory… (More)

- Marc Baboulin, Xiaoye S. Li, François-Henry Rouet
- VECPAR
- 2014

We consider the solution of sparse linear systems using direct methods via LU factorization. Unless the matrix is positive definite, numerical pivoting is usually needed to ensure stability, which is costly to implement especially in the sparse case. The Random Butterfly Transformations (RBT) technique provides an alternative to pivoting and is easily… (More)

- Kamer Kaya, François-Henry Rouet, Bora Uçar
- Euro-Par Workshops
- 2011

Hypergraph and graph partitioning tools are used to partition work for efficient parallelization of many sparse matrix computations. Most of the time, the objective function that is reduced by these tools relates to reducing the communication requirements, and the balancing constraints satisfied by these tools relate to balancing the work or memory… (More)

- Ichitaro Yamazaki, Xiaoye S. Li, François-Henry Rouet, Bora Uçar
- 2013 IEEE International Symposium on Parallel…
- 2013

PDSLin is a general-purpose algebraic parallel hybrid (direct/iterative) linear solver based on the Schur complement method. The most challenging step of the solver is the computation of a preconditioner based on the global Schur complement. Efficient parallel computation of the preconditioner gives rise to partitioning problems with sophisticated… (More)