BibTeX
@TECHREPORT{
         Fischer1987AdF,
       AUTHOR = "Fischer, Herbert",
       TITLE = "Automatic differentiation: {F}ast method to compute $f''(u)vv$ for given
         vector-valued $f$ and given $u$, $v$",
       TYPE = "Technical Report",
       INSTITUTION = "Technische Universt{\"a}t M{\"u}nchen, Institut
         f{\"u}r Angewandte Mathematik und Statistik",
       YEAR = "1987",
       KEYWORDS = "Differentiation arithmetic.",
       ABSTRACT = "Consider calculating the function $f''(u)vv$ for a given vector-valued f
         and given u, v, by using the affine function $ w: R \rightarrow R^n $ with $w(t) = u + t*v$, and the
         function $\psi: E \subseteq R \rightarrow R^n$ with $\psi(t) = f(w(t))$. Obviously
         $\psi''(0)11 = f''(u)vv =$ the vector wanted. The paper exploits this fact
         to produce a fast method for computing $f''(u)vv$. Operation counts are given for both the
         usual method and the fast method."
}