Details

Autor(en) / Beteiligte

• Kagiwada, Harriet
• Kalaba, Robert
• Rasakhoo, Nima
• Spingarn, Karl

Titel

Numerical Derivatives and Nonlinear Analysis [Elektronische Ressource]

Ist Teil von

• Mathematical Concepts and Methods in Science and Engineering : 31

Ort / Verlag

Boston, MA : Springer US

Erscheinungsjahr

1986

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• For many years it has been an article of faith of numerical analysts that the evaluation of derivatives of complicated functions should be avoided. Derivatives were evaluated using finite differences or, more recently, using symbolic manipulation packages. The first has the disadvantage of limited accuracy. The second has disadvantages of being expensive and requiring considerable computer memory. 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 Wengert over 20 years ago. 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 evalu~ ated 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