Aitken's method (convergence)?

Question

Newton's method does not converge quadratically for the following problem. Accelerate the convergence using the Aitken's (triangle in square) method.
Iterate until |q[n]-q[n-1]|<10^(-4);
for (x)^2 - 2*x*(e)^(-x) + e^(-2x)= 0, [0, 1]

Thank you for any provided info regarding this problem!!!

Answer 1

Aitken's method is lovely when you know what you are doing.

For a summary, take a look at:
http://mat.iitm.ac.in/~sryedida/caimna/transcendental/iteration%20methods/accelerating%20the%20convergence/aitken.html

For a little more explanation (a derivation, etc.), check out:
http://macs.citadel.edu/chenm/343.dir/07fal.dir/lect2_6.pdf

Answer 2

sophisticated subject. try searching in yahoo and bing. that will could help!