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Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation

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Xiong_Xin.pdf (2.23 MB)

Date

2014-01-23

Authors

Xiong, Xin

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University of Waterloo

Abstract

This 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.

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Keywords

Automatic differentiation, Forward mode, Reverse mode, Directed acyclic graph, Computational graph, Directed edge separator, Jacobian matrix, Newton step, Minimum cutset, Ford-Fulkerson algorithm, Sparsity technique, Hidden structure

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URI

http://hdl.handle.net/10012/8197

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Theses
Combinatorics and Optimization