The name is absent

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 x_n+1 is a
better approximation than x_n for the root x of the function f.

f(x∏)

^Xn ~ T7Γ~V
f (χ_n)

∆y ₌ f{χ_n) - 0

∆,τ x_n - x_n+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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