Nonlocal sensitivity analysis, automatic derivative evaluation, and sequential nonlinear estimation. (English) Zbl 0652.62081
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.
MSC:
| 62L12 | Sequential estimation |
| 62-04 | Software, source code, etc. for problems pertaining to statistics |
| 65C99 | Probabilistic methods, stochastic differential equations |
Keywords:
nonlocal sensitivity analysis; automatic derivative evaluation; sequential nonliner estimation; complete set of ordinary differential equations for generating solutions to parameterized systems of nonlinear equations; algorithm; exact evaluation of higher-order partial derivatives; general nonlinear least-squares estimationReferences:
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