Methods for Numerical Differentiation
It was in 1964 that R. Wengert (Reference 1) published a paper that showed how the partial derivatives of a given function could be evaluated by a computing machine without the user’s first having formed the analytical expressions for the desired derivatives. Furthermore, no use was made of symbol manipulation or finite difference approximations. A salient idea was that the computer was to do arithmetic, solely, and the user was to supply the needed “savvy” about differential calculus. In a companion paper (Reference 2) Wilkins discussed some practical considerations associated with the Wengert method. These two papers were studied intensely at the Rand Corporation for, at that time, there was great interest in orbit determination via quasilinearization (References 3 and 4). This resulted in a third early paper (Reference 3). A book was published in 1981 that described the situation to that date (Reference 5). A language known as PROSE also appeared.
KeywordsPartial Derivative Orbit Determination Call Statement Numerical Differentiation Differential Calculus
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- 3.BellmanR.,andKalaba, R.Quasilinearization and Nonlinear Boundary Value PatternsElsevier, New York, 1965.Google Scholar