Solving linear equation systems on vector computers with maximum efficiency (Q1110268)

The paper presents a technique for solving dense systems of linear equations by LU factorization on vector computers. Since LU factorization is one of the most widely used algorithms for solving linear dense systems, many implementations of it have been proposed in order to achieve good efficiency on various computers (for instance, LINPACK routines for use in a FORTRAN environment, use of SDOT BLAS, SAXPY BLAS, or Level 2 BLAS routines on supercomputers and non conventional architecture computers). The aim of the paper is to reach the maximum performance on processors like FPS-120, FPS-5000 and X64 series with the LU factorization algorithm using the FORTRAN language with calls to basic vector routines available in the mathematical library, without resorting to user-written assembly code. The FPS architecture allows to execute the dot-product operation (TMDOT routine) with peak performance by storing a vector in MD and the other one in TM, both with stride equal to 1. The proposed algorithm allows to solve a system of linear equations with asymptotic efficiency equal to 1 when N increases.