• openAccess   Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers 

      Anzt, Hartwig; Dongarra, Jack; Flegar, Goran; Higham, Nicholas J.; Quintana-Orti, Enrique S. Wiley (2019-03-25)
      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 double). ...
    • openAccess   Adaptive precision solvers for sparse linear systems 

      Anzt, Hartwig; Dongarra, Jack; Quintana-Orti, Enrique S. ACM (2015)
      We formulate an implementation of a Jacobi iterative solver for sparse linear systems that iterates the distinct components of the solution with different precision in terms of mantissa length. Starting with very low ...
    • closedAccess   Fine-grained bit-flip protection for relaxation methods 

      Anzt, Hartwig; Dongarra, Jack; Quintana-Ortí, Gregorio Elsevier (2019-09)
      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 part ...
    • closedAccess   Load-balancing Sparse Matrix Vector Product Kernels on GPUs 

      Anzt, Hartwig; Cojean, Terry; Yen-Chen, Chen; Dongarra, Jack; Flegar, Goran; Nayak, Pratik; Tomov, Stanimire; Tsai, Yuhsiang M.; Wang, Weichung Association for Computing Machinery (ACM) (2020-03)
      Efficient processing of Irregular Matrices on Single Instruction, Multiple Data (SIMD)-type architectures is a persistent challenge. Resolving it requires innovations in the development of data formats, computational ...
    • closedAccess   Tuning stationary iterative solvers for fault resilience 

      Anzt, Hartwig; Dongarra, Jack; Quintana-Orti, Enrique S. ACM. Association for Computing Machinery (2015)
      As the transistor’s feature size decreases following Moore’s Law, hardware will become more prone to permanent, intermittent, and transient errors, increasing the number of failures experienced by applications, and ...
    • closedAccess   Variable-size batched Gauss–Jordan elimination for block-Jacobi preconditioning on graphics processors 

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