The Solution of Partially Separable Linear Equations on Parallel Processing Systems

In this paper we consider the task of forming and solving the sets of linear equations that arise in the context of nonlinear problems. In particular we consider the fields of optimisation, ordinary differential equations and partial differential equations. We show that in each the system formation can be handled efficiently by automatic differentiation and quote results for the sparse doublet and sparse triplet implementations in Ada. Results are given that show that this can be very effectively performed on a parallel processing computer. The more recent reverse automatic differentiation approach is also discussed.