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We present a new algorithm to compute the QR factorization of a matrix Am×n intended for use when m ≫ n. The algorithm uses a reduction strategy to perform the factorization which in turn allows a good degree of parallelism. It is then integrated into a parallel implementation of the QR factorization with column pivoting algorithm due to Golub and Van Loan, which allows the determination of the rank...
We propose a new parallel domain decomposition algorithm to solve symmetric linear systems of equations derived from the discretization of PDEs on general unstructured grids of triangles or tetrahedra. The algorithm is based on a single-level Schwarz alternating procedure and a modified conjugate gradient solver. A single layer of overlap has been adopted in order to simplify the data-structure and...
Randomized algorithms are gaining ground in high-performance computing applications as they have the potential to outperform deterministic methods, while still providing accurate results. We propose a randomized solver for distributed multicore architectures to efficiently solve large dense symmetric indefinite linear systems that are encountered, for instance, in parameter estimation problems or...
Factorization of a dense symmetric indefinite matrix is a key computational kernel in many scientific and engineering simulations. However, there is no scalable factorization algorithm that takes advantage of the symmetry and guarantees numerical stability through pivoting at the same time. This is because such an algorithm exhibits many of the fundamental challenges in parallel programming like irregular...
We describe an efficient and innovative parallel tiled algorithm for solving symmetric indefinite systems on multicore architectures. This solver avoids pivoting by using a multiplicative preconditioning based on symmetric randomization. This randomization prevents the communication overhead due to pivoting, is computationally inexpensive and requires very little storage. Following randomization,...
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