Numerical Derivatives and Nonlinear Analysis

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

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 31)

Table of contents

  1. Front Matter
    Pages i-x
  2. Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
    Pages 1-13
  3. Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
    Pages 15-34
  4. Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
    Pages 35-109
  5. Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
    Pages 111-135
  6. Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
    Pages 137-166
  7. Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
    Pages 167-190
  8. Back Matter
    Pages 191-201

About this book

Introduction

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 pro­ grammed 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 im­ provements 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 deriva­ tive 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 sub­ routines. 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.

Keywords

Fortran computer control identification software

Authors and affiliations

  • Harriet Kagiwada
    • 1
  • Robert Kalaba
    • 1
  • Nima Rasakhoo
    • 1
  • Karl Spingarn
    • 1
  1. 1.Hughes Aircraft CompanyEl SegundoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-5056-9
  • Copyright Information Springer-Verlag US 1986
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-5058-3
  • Online ISBN 978-1-4684-5056-9
  • About this book