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1. Xiong, Xin. Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation.

Degree: 2014, University of Waterloo

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.

Subjects/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

…cannot be used for complicated computation due to space constraint, and the superior sparsity… …sparsity techniques are discussed in Chapter 4, followed by numerical experiments. In Chapter 5… …special technique can be used to greatly boost the efficiency. Main conclusions of the thesis… …x29;. Good methods that can exploit and take advantage of sparsity, constant values, and… …x29;. Generally speaking, in the presence of sparsity in J(x), the work required… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Xiong, X. (2014). Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/8197

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Xiong, Xin. “Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation.” 2014. Thesis, University of Waterloo. Accessed November 30, 2020. http://hdl.handle.net/10012/8197.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Xiong, Xin. “Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation.” 2014. Web. 30 Nov 2020.

Vancouver:

Xiong X. Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2020 Nov 30]. Available from: http://hdl.handle.net/10012/8197.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Xiong X. Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation. [Thesis]. University of Waterloo; 2014. Available from: http://hdl.handle.net/10012/8197

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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