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Numerical Derivatives and Nonlinear Analysis

- Book -
 

Author(s)
Harriet Kagiwada , Robert Kalaba , Nima Rasakhoo , Spingarn Karl

Year
1985

Publisher
Plenum Press, Inc.

Abstract
The authors survey automatic differentiation by the FEED (Fast and Efficient Evaluation of Derivatives) method and its applications. The user writes programs consisting of subroutine calls. The subroutines perform the necessary differentiation arithmetic. Applications include Newton and Halley methods for rootfinding, nonlinear least squares, optimal control of two point boundary value problems using Newton-Raphson and gradient methods, system identification, Sukhanov's variable initial value method for boundary value problems, and nonlinear integral equations. Most examples include Fortran or Basic programs. The FEED method is used to compute the derivatives required by a method, but no Taylor series techniques are illustrated.

BibTeX
@BOOK{
         Kagiwada1985NDa,
       AUTHOR = "Kagiwada, Harriet and Kalaba, Robert and Rasakhoo, Nima and Spingarn Karl",
       TITLE = "Numerical Derivatives and Nonlinear Analysis",
       PUBLISHER = "Plenum Press, Inc.",
       YEAR = "1985",
       VOLUME = "31",
       SERIES = "Mathematical Concepts and Methods in Science and Engineering",
       ADDRESS = "New York",
       REFERRED = "MR 87g 65002; [Corliss1988AoD]; [Neid87a]; [Neidinger1989ADa];
         [Tesfatsion1991AEo].",
       COMMENT = "Lower level treatment than [Rall1981ADT] of automatic differentiation. Lacks concept
         of a coder. More detailed examples with programs. Reviewed in SIAM Review by Andreas Griewank -- not
         a great book",
       KEYWORDS = "automatic differentiation.",
       ABSTRACT = "The authors survey automatic differentiation by the FEED (Fast and Efficient
         Evaluation of Derivatives) method and its applications. The user writes programs consisting of
         subroutine calls. The subroutines perform the necessary differentiation arithmetic. Applications
         include Newton and Halley methods for rootfinding, nonlinear least squares, optimal control of two
         point boundary value problems using Newton-Raphson and gradient methods, system identification,
         Sukhanov's variable initial value method for boundary value problems, and nonlinear integral
         equations. Most examples include Fortran or Basic programs. The FEED method is used to compute the
         derivatives required by a method, but no Taylor series techniques are illustrated."
}


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