Help with method(s) show an iterative method converges to a known fixed point

Question

Are there any general techniques that can be used to show that an iterative method converges to a (known) fixed point?. In my current situation, I know the exact fixed point, but I am unaware of a method to show that the algorithm will converge to the point with certainty.

If it helps, I am using the EM algorithm and am trying to show that the algorithm converges to the true (known in this case) MLE.

Thanks for the help.

Answer 1

It doesn't converge to the fixed point with certainty. The answer depends on the starting point. For a multi-modal distribution, it can converge to any local maximum. The general proof involves coupling co-ordinate ascent with strong duality. Check out the link below

http://web.stanford.edu/~lmackey/stats306b/doc/stats306b-spring14-lecture3_scribed.pdf