Automatic Differentiation of Computer Programs

Nonlocal automated comparative static analysis

“…A similar approach is suggested in refs. [19], [22], and [27, ments Feed in ADA, Jerrell [8] implements Feed in C++, and Wexler [34] implements Feed in C. One advantage of operator overloading is that expressions to be diiFerentiated can be written in a natural way; user-provided Wengert lists are not needed. Nevertheless, for clarity, the imple mentation of Feed for example (8) will be illustrated here using the simpler approach proposed in [16].…”

“…References to other work focusing on recurrence relations for the derivatives of special functions such as (11) can be found, for example, in ref. [19].…”

“…All of the numerical differentiation tests were performed on a Sun-3/260 workstation running SunOS UNIX To date, automatic differentiation studies (e.g., refs. [3,4,19,25,26,30,33]) have primarily emphasized the evaluation of first-order and possibly second-order partial derivatives. However, algorithms designed specific^y for the evaluation of higher-order partial derivatives are proposed in refs.…”

The AUGMENT precompiler as a tool for the development of special purpose arithmetic packages

“…Analytic differentiation of FORTRAN functions: This package, described in ( 10], allows one to obtain the Taylor Series expansion or the gradient of a function which can be expressed as a FORTRAN program . The technique is shown to be applicable to functions defined in terms of loops and conditional expressions as well as to the more conventional case of functions defined by a single FORTRAN statement .…”

Back Matter

“…[91] N. F. STEWART, A heuristic to reduce the wrapping effect in the numerical solution of BIT, 11 (1971) Differential equations, 70-72, 83-84, 93-115 Differential inequalities, [105][106][107][108][109][110][111][112][113][114] Ecosystems (application to) , [98][99]113 Ellipsoids, 17 Endpoints, 9 Equal intervals, 10 Excess width, 35,42,44,45,47,48,50 Exclusion tests, [76][77] Extended interval arithmetic, 17,65,[66][67][68] Finance (application to) , [117][118][119][120][121][122][123] Finite convergence, 36-38, 51, 53, 56 Inclusion monotonicity, [20][21]22,23,24,29,35,41,51,52,63,[69][70][93][94][95]…”