17
Figure 2.2: An Illustration of One Iteration of Newton’s Method
The function f is shown in blue and the tangent line is in red. We see that xn+1 is a
better approximation than xn for the root x of the function f.
f(x∏)
(2.3)
(2.4)
Xn ~ T7Γ~V
f (χn)
∆y = f{χn) - 0
∆,τ xn - xn+1 '
The method will usually converge, provided the initial guess is close enough to
the true root, and that ∕7(x0) ≠ θ∙
Newton’s method is used in this research to maximize the extended partial like-
lihood function in order to get optimal parameter estimates. See details in Section
3.3.4.
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