Numerical derivatives and nonlinear analysis
Numerical derivatives and nonlinear analysis
More test examples for nonlinear programming codes
More test examples for nonlinear programming codes
Automatic Differentiation of Computer Programs
ACM Transactions on Mathematical Software (TOMS)
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Automatic Differentiation and Interval Arithmetic for Estimation of Disequilibrium Models
Computational Economics - Special issue on computational economics in Geneva: volume 1: computational econometrics, statistics, and optimization
Remark on algorithm 746: new features of PCOMP, a Fortran code for automatic differentiation
ACM Transactions on Mathematical Software (TOMS)
Data fitting in partial differential algebraic equations: some academic and industrial applications
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
EASY-FIT: a software system for data fitting in dynamical systems
Structural and Multidisciplinary Optimization
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Automatic differentiation is an interesting and important tool for all numerical algorithms that require derivatives, e.g., in nonlinear programming, optimal control, parameter estimation, and differential equations. The basic idea is to avoid not only numerical approximations, which are expensive with respect to CPU time and contain round-off errors, but also hand-coded differentiation. This article introduces the forward and backward accumulation methods and describes the numerical implementation of a computer code with the name PCOMP. The main intention of the approach used is to provide a flexible and portable Fortran code for practical applications. The underlying language is described in terms of a formal grammar and is a subset of Fortran with a few extensions. Besides a parser that generates an intermediate code and that can be executed independently from the evaluation routines, there are other subroutines for the direct computation of function and gradient values, which can be called directly from a user program. On the other hand, it is possible to generate a Fortran code for function and gradient evaluation that can be compiled and linked separately.