Newton's method in Matlab

I need to apply Newton's Method in Matlab to the function f(x)= a-(1/x) to show how a program which cannot do division can be used to compute 1/a for a>0. How would I proceed? Thanks.

Answer 1

[Thorsten]

Approximation of 1/a by x using a suitable starting value x = 0.1:

 a = 14; x = 0.1; while abs(x*a - 1) > eps,  x = x*(2-a*x), end

[piniaw15]

Hi, I used newtons method to get to x = x*(2-a*x)

But I don't understand what you've done here: abs(x*a - 1) > eps Can you explain please?

[Thorsten]

The value x should approximate 1/a, so x*a should approximate 1, or abs(x*a - 1) should approximate 0. I don't check for 0 because this is numerically not stable; instead, I check against the machine precision eps. The loop continuos until this precision is reached. If you need less precision, you could use, e.g.

while abs(x*a - 1) > 1e-6,