Nonlocal sensitivity analysis, automatic derivative evaluation, and sequential nonlinear estimation (Q1107245)

The present paper summarizes recent work by the authors on computational methods for nonlinear processes. Section 2 develops a complete set of ordinary differential equations for generating solutions to parameterized systems of nonlinear equations over parameter intervals of interest. Section 3 presents a simple finite algorithm for the systematic exact evaluation of higher-order partial derivatives. Section 4 obtains an exact sequential characterization for the solution to a general nonlinear least-squares estimation problem as the duration of the process increases and additional observations are made.