Hyper - Systolic Implementation of BLAS - 3 Routines on the APE 100 / Quadrics

Basic Linear Algebra Subroutines (BLAS-3) 1] are building blocks to solve a lot of numerical problems (Cholesky factorization, Gram-Schmidt ortonormalization, LU decomposition,...). Their eecient implementation on a given parallel machine is a key issue for the maximal exploitation of the system's computational power. In this work we refer to a massively parallel processing SIMD machine (the APE100/Quadrics 2]) and to the adoption of the hyper-systolic method 3, 6, 4] to eeciently implement BLAS-3 on such a machine. The results we achieved (nearly 60-70% of the peak performances for large matrices) demonstrate the validity of the proposed approach. The work is structured as follows: section 1 is devoted to review BLAS-3, in section 2 we recall the hyper-systolic method, subsequently (section 3), the target machine is described and (section 4) the HS implementation is shown. Finally (section 5), some experimental results are given.