Could someone please so me how Newton's Method is used in Numerical Analysis? My teacher is doing a horrible job of teaching it and he skips a lot of steps.
Newtons Method:
X(n+1) = x(n) - f(x(n))/f'(x(n)) (n) is a subcript to x.
Could someone please so me how Newton's Method is used in Numerical Analysis? My teacher is doing a horrible job of teaching it and he skips a lot of steps.
Newtons Method:
X(n+1) = x(n) - f(x(n))/f'(x(n)) (n) is a subcript to x.
It is a method to find the solutions to a function using the derivative and the original function only
For example consider $\displaystyle x^4-3x^3+17\sin(x)=0$
We have to make an initial guess..lets say 2
So we set up our first iteration
$\displaystyle x_1=2-\frac{(2)^4-3(2)^4+17\sin(2)}{4(2)^2-9(2)^2+17\cos(2)}=\psi$
C is just because I dont have my calculator
So then
$\displaystyle x_2=\psi-\frac{\psi^4-3\psi^4+17\sin(\psi))}{4\psi^3-9\psi^2+17\cos(\psi)}$
and then obviously
$\displaystyle x_n=\psi_n-\frac{\psi_n^4-3\psi_n^3+17\sin(\psi_n)}{4\psi_n^3-9\psi_n^2+17\cos(\psi_n)}$
and as $\displaystyle n\to\infty$ the iterations will yield that zero of th function