Complex Systems

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

Stanislaw Osowski
Institute of the Theory of Electrical Engineering,
and Electrical Measurements, Technical University,
00-661 Warsaw, pl. Politechniki 1, Poland

Jeanny Herault
Laboratoire TIRF, INPG,
46, av. F. Viallet, 38031 Grenoble, France


This paper presents the application of signal flow graphs to the determination of the exact values of gradient vector and hessian matrix for a linear system. It is shown all information about the gradient and hessian is contained in the original and adjoint signal flow graphs at different terminations. To determine the gradient we have to perform two analyses, and to get the full hessian matrix we perform analyses of the graph (or the system), where is the number of internal nodes of the graph. The examples included in the paper illustrate the method.