Solving linear equation systems on vector computers with maximum efficiency

A technique is presented for solving dense systems of linear equations by LU factorization with maximum performance on processors like FPS-120, FPS-5000 and X64 series, using FORTRAN with calls to elementary vector routines. A rearrangement of the matrix elements is done in order to compute all the matrix-vector operations involved in the LU factorization with only stride-1 dot-product operations, which are executed at peak speed in the FPS processors. Since only vector instructions are used, the algorithm is fully portable on all FPS 38/64 bit machines and in general on all vector computers with a similar memory structure. The performance obtained on FPS-100 and FPS M64/60 (FPS-264) processors is reported: the asymptotic speed is always the peak speed of the machine and the half performance length is N_1/2 = 238 for the FPS-100 and N_1/2 = 200 for the FFS M64/60. The N_1/2 vaLues could he lowered by using the APAL Assembly Language to code some critical parts, losing however the code portability.