Showing papers on "Degree of parallelism published in 1973"
01 Dec 1973
TL;DR: In this paper, a parallel variable metric algorithm was proposed to exploit parallel computing or vector streaming (pipeline) capabilities of computers, and the convergence of the iterates to the solution was proved for a quadratic functional on a real separable Hilbert space.
Abstract: An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.
37 citations