This article surveys work by the authors on new tools for the calculation and tracking of solutions for nonlinear parameterized systems. Annotated pointers to related work can be accessed at: http://www.econ.iastate.edu/tesfatsi/nasahome.htm http://www.econ.iastate.edu/tesfatsi/flshome.htm

This article develops an algorithm for the exact forward-mode automatic evaluation of higher order partial derivatives using derivative arrays, now referred to as the FEED (Fast Efficient Evaluation of Derivatives) algorithm. Building on previous work by R. Wengert, the FEED algorithm proceeds...