Automation of Nested Matrix and Derivative Operations

In Kalaba, Tesfatsion, and Wang (JMAA,1983) an algorithm was developed for the exact forward-mode automatic evaluation of higher-order partial derivatives of functions of many variables using derivative arrays. This algorithm was supported by a library of "calculus subroutines" for many standard one-variable and two-variable functions. This article extends the FEED library to permit the automatic differentiation of expressions involving nested matrix and derivative operations. The need to differentiate such expressions arose naturally in the course of designing sequential filters for a class of nonlinear tracking problems. Annotated pointers to related work can be accessed at: http://www.econ.iastate.edu/tesfatsi/nasahome.htm