Xiong, Xin2014-01-232014-01-232014-01-232014http://hdl.handle.net/10012/8197This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of two directed edge separator methods, the weighted minimum separator and natural order separator methods, to exploit the structure of the computational graph of the nonlinear system.This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments.enAutomatic differentiationForward modeReverse modeDirected acyclic graphComputational graphDirected edge separatorJacobian matrixNewton stepMinimum cutsetFord-Fulkerson algorithmSparsity techniqueHidden structureMaster ThesisCombinatorics and Optimization