Introductory Programming
Fall 2005

Evaluation 9 on Thursday!

Try this at the MATLAB prompt:

format long
a = 4
x = a
x = (x + a/x) / 2

Repeat the last line several times and see how quickly it
converges on the right answer.

Why does this work?

Here's a function that implements this technique:

function r = newton (a)
% r = newton (a)
% return an approximation of the square root of a
x = a;
for j = 1:5
    x = 1/2 * (x + a/x);
    fprintf ('j = %f   x = %f\n', j, x)
end
r = x;

What if it takes more than 5 iterations to converge?

Why not just use fzero?

How can we use this technique more generally?

Find as many roots as you can of e^x - 3 x^2 = 0