An ADA library for automatic evaluation of derivatives

摘要

Requirements for the evaluation of high-order partial derivatives arise in many applications, including optimal control, system identification, and the numerical solution of nonlinear algebraic equations, two-point boundary-value problems, and integral equations. These evaluations have long been shunned by numerical analysts because of the difficulty in forming symbolic expressions for the derivatives. This paper describes in detail an implementation in ADA of a set of simple procedures for evaluating derivatives exactly, without the requirement to form their symbolic expressions and without resorting to finite-difference methods. An expression whose derivatives are desired is written in the usual way, using standard mathematical operators and intrinsic functions, and values of all desired derivatives are returned automatically. Two examples of parameter identification are shown, one from economics and one from guidance and control. A complete listing of all ADA code is included.