An iterative solution to speical linear systems on a vector hypercube

Abstract

An Intel Hypercube implementation of a new stationary iterative method developed by one of us (JdP) is presented. This algorithm finds the solution vector x for the invertible n × n linear system Ax = (I - B)x = f where A has real spectrum. The solution method converges quickly because the Jacobi iteration matrix B is replaced by an equivalent iteration matrix with a smaller spectral radius. The parallel algorithm partitions A row-wise among all the processors in order to keep memory load to a minimum and to avoid duplicate computations. With the introduction of vector hardware to the Hypercube, more modifications have been made to the implementation algorithm in order to exploit that hardware and reduce run-time even further. Example problems and timings will be presented.