Publication: Solution of nonlinear systems of equations on the FPS 64-bit family of scientific computers using automatic differentiation
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Solution of nonlinear systems of equations on the FPS 64-bit family of scientific computers using automatic differentiation

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Author(s)
Bradley R. Carlile

Published in
Proceedings of the 1986 Array Conference (Portland, Oregon)

Year
1986

Abstract
The author considers the solution of nonlinear equations using Newton's method. He presents a method which uses differentiation arithmetic to calculate the Jacobian which is required. This method is compared with a finite differencing approach to calculating the Jacobian on a short pipeline machine, the FPS. The differentiation arithmetic approach outperforms the finite differencing approach on all of the test problems presented solving two of the problems which the finite differencing approach failed to solve.

BibTeX
@INPROCEEDINGS{
         Carlile1986Son,
       AUTHOR = "Carlile, Bradley R.",
       TITLE = "Solution of nonlinear systems of equations on the {FPS} 64-bit family of scientific
         computers using automatic differentiation",
       BOOKTITLE = "Proceedings of the 1986 Array Conference (Portland, Oregon)",
       YEAR = "1986",
       PAGES = "142--169",
       KEYWORDS = "point algorithm; differentiation arithmetic; nonlinear equations; numerical
         results; computer program.",
       ABSTRACT = "The author considers the solution of nonlinear equations using Newton's
         method. He presents a method which uses differentiation arithmetic to calculate the Jacobian which
         is required. This method is compared with a finite differencing approach to calculating the Jacobian
         on a short pipeline machine, the FPS. The differentiation arithmetic approach outperforms the finite
         differencing approach on all of the test problems presented solving two of the problems which the
         finite differencing approach failed to solve."
}


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