Differentiation by Forward Finite Differences

The relationships between forward difference operators and differential operators, which are summarized in Table 3.2, enable us to develop a variety of formulas expressing derivatives of functions in terms of forward finite differences and vice versa. As was demonstrated in Sec. 4.2, these formulas may have any degree of accuracy desired, provided that a sufficient number of terms are retained in the manipulation of these infinite series. A set of expressions, parallel to those of Sec. 4,2, will be derived using the forward finite differences. 

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Method of Solution The Marquardt method using the Gauss-Newton technique, described in Sec. 7.4.4, and the concept of multiple nonlinear regression, covered in Sec. 7.4.5, have been combined together to solve this example. Numerical differentiation by forward finite differences is used to evaluate the Jacobian matrix defined by Eq. (7.164). 

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