Automatic Differentiation for Gradients, Jacobians, and Hessians

Ulrich Kulisch, Rolf Hammer, Matthias Hocks and Dietmar Ratz
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Ulrich Kulisch: Universität Karlsruhe, Institut für Angewandte Mathematik
Rolf Hammer: Universität Karlsruhe, Institut für Angewandte Mathematik
Matthias Hocks: Universität Karlsruhe, Institut für Angewandte Mathematik
Dietmar Ratz: Universität Karlsruhe, Institut für Angewandte Mathematik

Chapter Chapter 12 in C++ Toolbox for Verified Computing I, 1995, pp 244-292 from Springer

Abstract: Abstract In Chapter 5, we considered automatic differentiation in one variable, but there are also many applications of numerical and scientific computing where it is necessary to compute derivatives of multi-dimensional functions. In this chapter, we extend the concept of automatic differentiation to the multi-dimensional case as given by Rail [72] and many others. We apply well-known differentiation rules for gradients, Jacobians, or Hessians with the computation of numerical values, combining the advantages of symbolic and numerical differentiation. Only the algorithm or formula for the function is required. No explicit formulas for the gradient, Jacobian, or Hessian have to be derived and coded.

Keywords: Jacobian Matrix; Hessian Matrix; Interval Arithmetic; Lower Triangular Matrix; Automatic Differentiation (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-3-642-79651-7_12

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