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Number 2 - June 2019
Volume 29 - 2019
The parallel tiled WZ factorization algorithm for multicore architectures
Beata Bylina, Jarosław Bylina
Abstract
The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The
design and implementation of a parallel tiled WZ factorization algorithm which can fully exploit such architectures are
presented. Three parallel implementations of the algorithm are studied. The first one relies only on exploiting multithreaded
BLAS (basic linear algebra subprograms) operations. The second implementation, except for BLAS operations, employs
the OpenMP standard to use the loop-level parallelism. The third implementation, except for BLAS operations, employs
the OpenMP task directive with the depend clause. We report the computational performance and the speedup of the parallel tiled WZ factorization algorithm on shared memory multicore architectures for dense square diagonally dominant matrices. Then we compare our parallel implementations with the respective LU factorization from a vendor implemented LAPACK library. We also analyze the numerical accuracy. Two of our implementations can be achieved with near maximal
theoretical speedup implied by Amdahl’s law.
Keywords
tiled algorithm, WZ factorization, solution of linear systems, Amdahl’s law, high performance computing, multicore architectures