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Algorithms come with multiple variants which are obtained by changing the mathematical approach from which the algorithm is derived. These variants offer a wide spectrum of performance when implemented on a multicore platform and we seek to understand these differences in performances from a theoretical point of view. To that aim, we derive and present the… (More)

This work revisits existing algorithms for the QR factorization of rectangular matrices composed of <i>p</i> × <i>q</i> tiles, where <i>p</i> ≥ <i>q.</i> Within this framework, we study the critical paths and performance of algorithms such as Sameh-Kuck, Fibonacci, Greedy, and those found within PLASMA. Although neither Fibonacci nor Greedy is… (More)

The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research has shown that it is possible to write efficient and scalable tile algorithms for performing a Cholesky factorization, a… (More)

We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid when used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsen-ing Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants… (More)

Current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core architectures. A new family of algorithms, the tile algorithms, has recently been introduced to circumvent this problem. Previous… (More)

We analyze a possibility of turning off post-smoothing (relaxation) in geometric multigrid when used as a preconditioner in preconditioned conjugate gradient (PCG) linear and eigen-value solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two… (More)

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