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.
Solving linear equation systems on vector computers with maximum efficiency
Corana A;Martini C;Morando M;
1988
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.