A potential problem in implementing the Newton-Raphson method is the
evaluation of the derivative. Although this is not inconvenient for polynomials
and many other functions, there are certain functions whose derivatives may be
extremely difficult or inconvenient to evaluate. For these cases, the
derivative can be approximated by a backward finite divided difference, as in
This approximation can
be substituted to yield the following it equation:
Equation is the formula for the secant method. Notice
that the approach requires two
Initial estimates of x. However, because f(x) is not required
to change signs between
the estimates, it is not classified as a bracketing
method.
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