New techniques for fast hybrid solutions of systems of equations

Abstract

A fast analogue solver with limited precision is used as a preconditioner in an iterative process which develops full digital precision. This hybrid process is highly parallel, and, in principle, it can be faster than digital computations alone. A problematic feature of this process is that the low analogue precision can adversely affect convergence speed. New techniques are introduced to address this limitation. A partial separation of analogue imprecision and poor problem condition is made. Fully parallel digital (smoothing) iterations are introduced to eliminate the effect of random errors which accompany analogue–digital conversion. Application is made to the problem of repeated summation. Copyright © 1989 John Wiley & Sons, Ltd