Numerical derivatives and nonlinear analysis
type: Item
instance of: scholarly article
title: Numerical derivatives and nonlinear analysis
zbMATH Open document ID: 0665.65017
author: Nima Rasakhoo
author: Karl Spingarn
author: Harriet H. Kagiwada
author: R. E. Kalaba
published in: Mathematical Concepts and Methods in Science and Engineering
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 4088814
zbMATH Keywords: automatic derivative evaluation subroutines
zbMATH Keywords: FORTRAN
zbMATH Keywords: BASIC
zbMATH Keywords: Wengert's method
zbMATH Keywords: partial derivatives
zbMATH Keywords: nonlinear least-squares
zbMATH Keywords: optimal control
zbMATH Keywords: system identification
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4088814