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A generalised Newton algorithm using higher-order derivatives

- Article in a journal -

Published in
J. Opt. Theory and Appl.

Year
1983

Abstract
A Newton-type algorithm which uses first to rth order partial derivatives is described. This reduces to the Newton-Raphson algorithm if r = 2 . The partial derivatives are calculated using the table method described in [Kalaba1983AFA]. A specific example is given to show that the convergence of the method is faster than that of the standard Newton-Raphson algorithm.

BibTeX
@ARTICLE{
         Kalaba1983AgN,
       AUTHOR = "Kalaba, Robert and Tishler, A.",
       TITLE = "A generalised {N}ewton algorithm using higher-order derivatives",
       JOURNAL = "J. Opt. Theory and Appl.",
       VOLUME = "39",
       NUMBER = "1",
       YEAR = "1983",
       PAGES = "1--17",
       KEYWORDS = "point algorithm; differentiation arithmetic; root finding.",
       ABSTRACT = "A Newton-type algorithm which uses first to rth order partial derivatives is
         described. This reduces to the Newton-Raphson algorithm if $ r = 2 $ . The partial derivatives are
         calculated using the table method described in [Kalaba1983AFA]. A specific example is given to show
         that the convergence of the method is faster than that of the standard Newton-Raphson algorithm."
}

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