Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis is concerned with the efficient computation of Jacobian matrices of nonlin-ear vector maps using automatic differentiation (AD). Specificially, 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 computional graph of the nonlinear sys-tem. This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments. iii Acknowledgements I am heartily thankful to my supervisor, Thomas F. Coleman, whose encouragement, guidance and support from the initial to the final level enabled me to develop an under