P. Habala, DEN-07d: Root finding - Fixed point iteration

“Differential equations and numerical analysis” is a course offering a basic overview of these two fields. The original lectures were partially reshot and augmented to offer more for those who need to/like to explore the topics further.
[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
[1:05:54] Relaxation, example
[1:18:34] Optimising the relaxation parameter
[1:27:42] Root finding through fixed points, relaxation for root problems
[1:34:04] Experiments
[1:05:54] Relaxation, example
[1:16:40] Optimising the relaxation parameter
[1:27:43] Root finding through fixed points, relaxation for root problems
[1:34:04] Experiments
Complete playlist: • doc. P. Habala: Differ...