Answer to Question #263131 in Quantitative Methods for Amrit

Question

Let f(x) =x²-a. Show that the Newton-raphson method leads to the recurrent

Answer 1

A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones.

by the Newton-Raphson method:

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

$f'(x)=2x$

recurrence relation:

$x_{n+1}=x_n-\frac{x_n^2-a}{2x_n}$