Hierarchical Approach for Deriving a Reproducible LU factorization

Roman Iakymchuk (1) , Stef Graillat (2) , David Defour (3) , Erwin S Laure (1) , Enrique S Quintana-Ortí (4)

1 KTH - KTH Royal Institute of Technology [Stockholm]
2 PEQUAN - Performance et Qualité des Algorithmes Numériques
3 DALI - Digits, Architectures et Logiciels Informatiques
4 Universitat Jaume I = Jaume I University

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 the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated into a (blocked) high performance and stable algorithm for the LU factorization.

Mots clés: accuracy; long accumulator; error-free transformation; GPUs; LU factorization; BLAS; reproducibility

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Arithmétique des ordinateurs

Roman Iakymchuk, Stef Graillat, David Defour, Erwin S Laure, Enrique S Quintana-Ortí. Hierarchical Approach for Deriving a Reproducible LU factorization. 2016. ⟨hal-01419813v1⟩