Automation of nested matrix and derivative operations

摘要

In 1983 an algorithm feed was introduced for the systematic exact evaluation of higher-order partial derivatives of functions of many variables. In 1986 the feed library was extended to permit the automatic differentiation of functions expressed in terms of the derivatives of other functions. Building on this work, the present paper further 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.