Newton's method

[shiditso]

Apply Newton's method to the equation x^2-a=0 to derive the following square-root algorithm:

x(n+1)=(1/2)(xn+9a/xn)

I am not really sure where to begin. I know the equation for Newton's method is x(n+1)=xn-(f(xn)/f'(xn)). I do no know what I nee dot do or where to begin...

 

[Deleted member 4993]

Apply Newton's method to the equation x^2-a=0 to derive the following square-root algorithm:

x(n+1)=(1/2)(xn+9a/xn)

I am not really sure where to begin. I know the equation for Newton's method is x(n+1)=xn-(f(xn)/f'(xn)). I do no know what I nee dot do or where to begin...

f(x) = x[sup:2unfzi3d]2[/sup:2unfzi3d] - a

f'(x) = 2*x

Then

x[sub:2unfzi3d]n+1[/sub:2unfzi3d] = x[sub:2unfzi3d]n[/sub:2unfzi3d] - f(x[sub:2unfzi3d]n[/sub:2unfzi3d])/f'(x[sub:2unfzi3d]n[/sub:2unfzi3d])

f(x[sub:2unfzi3d]n[/sub:2unfzi3d]) = x[sub:2unfzi3d]n[/sub:2unfzi3d][sup:2unfzi3d]2[/sup:2unfzi3d] - a

Now continue.....

.

 

[shiditso]

Thanks a bunch!