Root finding: Fixed point iteration 

[0:00:05] Intro, fixed points
[0:09:54] Existence of fixed points
[0:16:55] Simple iteration, yields fixed points if convergent
[0:30:26] Convergence of iteration, contraction
[0:37:11] The Banach contraction theorem with proof, derivative test, example
[0:53:01] Graph interpretation of iteration, typical behaviour
[1:05:58] Relaxation, example
[1:19:03] Optimising the relaxation parameter
[1:28:10] Root finding through fixed points, relaxation for root problems
[1:34:32] Experiments
For the complete course, see the playlist
• doc. P. Habala: Differ...