Numerical derivatives and nonlinear analysis
The recent developments described in this text allow the evaluation of derivatives using simple automatic derivative evaluation subroutines programmed in FORTRAN or BASIC. These subroutines can even be programmed on a personal computer. The concept for the evaluation of the derivatives was originally developed by \textit{R. E. Wengert} [Commun. ACM 7, 463-464 (1964; Zbl 0131.346)]. Significant improvements have been made in Wengert's method and are utilized in this text. The purpose of this text is to familiarize computer users with a simple and practical method for obtaining the partial derivatives of complicated mathematical expressions. The text illustrates the use of automatic derivative evaluation subroutines to solve a wide range of nonlinear least-squares, optimal control, system identification, two-point boundary value problems, and integral equations. The numerical values of the derivatives are evaluated exactly, except for roundoff, using simple FORTRAN or BASIC subroutines. These derivatives are derived automatically behind the scenes, from the equivalent of analytical expressions, without any effort from the user. The use of costly software packages is not required. In many cases, such as in optimization problems, the user of the program need only enter an analytical expression into the program. The derivatives as well as the complete solution are then evaluated automatically.
automatic derivative evaluation subroutines
scientific article; zbMATH DE number 4088814