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Methods for Numerical Differentiation

  • Harriet Kagiwada
  • Robert Kalaba
  • Nima Rasakhoo
  • Karl Spingarn
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 31)

Abstract

It was in 1964 that R. Wengert (Reference 1) published a paper that showed how the partial derivatives of a given function could be evaluated by a computing machine without the user’s first having formed the analytical expressions for the desired derivatives. Furthermore, no use was made of symbol manipulation or finite difference approximations. A salient idea was that the computer was to do arithmetic, solely, and the user was to supply the needed “savvy” about differential calculus. In a companion paper (Reference 2) Wilkins discussed some practical considerations associated with the Wengert method. These two papers were studied intensely at the Rand Corporation for, at that time, there was great interest in orbit determination via quasilinearization (References 3 and 4). This resulted in a third early paper (Reference 3). A book was published in 1981 that described the situation to that date (Reference 5). A language known as PROSE also appeared.

Keywords

Partial Derivative Orbit Determination Call Statement Numerical Differentiation Differential Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Chapter 1

  1. 1.
    Wengert, R. E., A simple automatic derivative evaluation program, Communications of the ACM ,Vol. 7, No. 8, pp. 463–464, August 1964.MATHCrossRefGoogle Scholar
  2. 2.
    Wilkins, R. D., Investigation of a new analytical method for numerical derivative evaluation, Communications of the ACM ,Vol. 7, No. 8, pp. 465–471, August 1964.MATHCrossRefGoogle Scholar
  3. 3.
    BellmanR.,andKalaba, R.Quasilinearization and Nonlinear Boundary Value PatternsElsevier, New York, 1965.Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

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

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