Signal Flow Graphs as an Efficient Tool for Gradient and Exact Hessian Determination

Abst ract. This pap er pr esents th e applica tion of signal flow gra phs to the det ermination of the exact values of gradient vecto r and hessian matrix for a linear system. It is shown all information about the gradient and hessian is cont ained in the or iginal and adjoint signa l flow graphs at different terminations. To det ermine the gra dient we have to perform two analyses , and t o get the full hessian matrix we perform (2K + 1) ana lyses of the graph (or t he system), where K is the nu mb er of internal nodes of the graph . T he examples included in the pap er illust rate the met hod.