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Browsing by Subject "Sparse linear systems"

Now showing items 1-8 of 8

Accelerating the task/data-parallel version of ILUPACK¿s BiCG in multi-CPU/GPU configurations

Aliaga, Jose I.; Dufrechou, Ernesto; Ezzatti, Pablo; Quintana-Ortí, Enrique S. (Elsevier, 2019-07)

[EN] ILUPACK is a valuable tool for the solution of sparse linear systems via iterative Krylov subspace-based methods. Its relevance for the solution of real problems has motivated several efforts to enhance its performance ...
Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers

Anzt, Hartwig; Dongarra, Jack; Flegar, Goran; Higham, Nicholas J.; Quintana Ortí, Enrique Salvador (John Wiley & Sons, 2019-03-25)

[EN] We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block-Jacobi preconditioner in different precision formats (half, single, or ...
Balanced incomplete factorization preconditioner with pivoting

Marín Mateos-Aparicio, José; Mas Marí, José (Springer-Verlag, 2023-01)

[EN] In this work we study pivoting strategies for the preconditioner presented in Bru (SIAM J Sci Comput 30(5):2302-2318, 2008) which computes the LU factorization of a matrix A. This preconditioner is based on the Inverse ...
Fine-grained bit-flip protection for relaxation methods

Anzt, Hartwig; Dongarra, Jack; Quintana Ortí, Enrique Salvador (Elsevier, 2019-09)

[EN] Resilience is considered a challenging under-addressed issue that the high performance computing community (HPC) will have to face in order to produce reliable Exascale systems by the beginning of the next decade. As ...
Low-rank updates of balanced incomplete factorization preconditioners

Cerdán Soriano, Juana Mercedes; Marín Mateos-Aparicio, José; Mas Marí, José (Springer-Verlag, 2017)

[EN] Let Ax = b be a large and sparse system of linear equations where A is a nonsingular matrix. An approximate solution is frequently obtained by applying preconditioned terations. Consider the matrix B = A + PQT where ...
Preconditioners for nonsymmetric linear systems with low-rank skew-symmetric part

Cerdán Soriano, Juana Mercedes; Guerrero-Flores, Danny Joel; Marín Mateos-Aparicio, José; Mas Marí, José (Elsevier, 2018-12-01)

[EN] We present a preconditioning technique for solving nonsymmetric linear systems Ax = b, where the coefficient matrix A has a skew-symmetric part that can be well approximated with a skew-symmetric low-rank matrix. The ...
Preconditioners for rank deficient least squares problems

Cerdán Soriano, Juana Mercedes; Guerrero, D.; Marín Mateos-Aparicio, José; Mas Marí, José (Elsevier, 2020-07)

[EN] In this paper we present a method for computing sparse preconditioners for iteratively solving rank deficient least squares problems (LS) by the LSMR method. The main idea of the method proposed is to update an ...
Variable-size batched Gauss-Jordan elimination for block-Jacobi preconditioning on graphics processors

Anzt, Hartwig; Dongarra, Jack; Flegar, Goran; Quintana Ortí, Enrique S. (Elsevier, 2019-01)

[EN] In this work, we address the efficient realization of block-Jacobi preconditioning on graphics processing units (GPUs). This task requires the solution of a collection of small and independent linear systems. To fully ...