• openAccess   General Framework for Deriving Reproducible Krylov Subspace Algorithms: BiCGStab Case 

      Iakymchuk, Roman; Graillat, Stef; Aliaga Estellés, José Ignacio Springer (2023)
      Parallel implementations of Krylov subspace algorithms often help to accelerate the procedure to find the solution of a linear system. However, from the other side, such parallelization coupled with asynchronous and ...
    • openAccess   Hierarchical approach for deriving a reproducible unblocked LU factorization 

      Iakymchuk, Roman; Graillat, Stef; Defour, David; Quintana-Orti, Enrique S. Sage (2019-03-17)
      We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for ...
    • openAccess   Reproducibility of parallel preconditioned conjugate gradient in hybrid programming environments 

      Iakymchuk, Roman; Barreda Vayá, Maria; Graillat, Stef; Aliaga Estellés, José Ignacio; Quintana-Orti, Enrique S. Sage (2020-06-17)
      The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for ...
    • closedAccess   Reproducibility strategies for parallel Preconditioned Conjugate Gradient 

      Iakymchuk, Roman; Barreda Vayá, Maria; Wiesenberger, Matthias; Aliaga Estellés, José Ignacio; Quintana-Orti, Enrique S. Elsevier (2020-01-02)
      The Preconditioned Conjugate Gradient method is often used in numerical simulations. While being widely used, the solver is also known for its lack of accuracy while computing the residual. In this article, we aim at a ...