Applications of Software for Automatic Differentiation in Numerical Computation.
Abstract
At present, software for formula translation is used routinely in numerical computation. On the other hand, although software for differentiation of formulas is easy to construct and widely available, many numerical analysts seem to be unaware of its existence and potential for numerical computation. A simple procedure for formula translation and differentiation will be described, and some significant applications will be indicated. In ordinary computation, these include solution of ordinary and partial differential equations by series methods (Taylor and Lie series, for example), solution of nonlinear systems of equations by Newton's method and its variants, and nonlinear optimization (constrained and unconstrained). Together with interval analysis, differentiation can be used to determine properties of functions and thus automate the application of certain theorems, such as ones for existence of fixed points of n-dimensional operators or solutions of nonlinear systems of equations. Another large field of application of differentiation is to automatic error analysis, either using the graph structure of the computation, or interval analysis. An example is given of a program for numerical integration in which automatic differentiation and interval analysis are combined to provide a priori and a posteriori error bounds for the results.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA077121
Entities
People
- Louis B. Rall
Organizations
- University of Wisconsin–Madison