initial guess
[initial guess|initial guess] Newton's method defines each subsequent approximation in terms of the previous one using the same formula.
Definition
initial guess Newton's method defines each subsequent approximation in terms of the previous one using the same formula. The initial guess must not be the exact root.
Mechanism
initial guess describes two scenarios where initial guesses lead to different convergence behaviors. In Example 4.49, the initial guess xq produces a sequence approaching a finite value through function F. In Example 4.48, the initial guess xg results in oscillating approximations between two values without converging to a root.
Effects
initial guess The initial guess xq in Example 4.49 leads to a resulting list of numbers approaching a finite value through a function F. In contrast, the initial guess xg in Example 4.48 results in successive approximations that alternate between two values without converging to a root.