We measure the rate of convergence of a fixed-point iteration process to the root of a cubic equation, without using any advanced techniques such as the mean value theorem.
How can you tell that a fixed-point iteration will converge?
https://youtu.be/K5k-mAgH3BE
This video was inspired by a similar example which appears here:
Hirst, K., 1994. Numbers, Sequences and Series. Butterworth-Heinemann.
00:00 Intro
01:10 Setup
02:58 Calculating |x_{n+1} - α|
05:52 Inequalities for α & x_n
09:54 Rate of convergence to α
13:56 Interpretation & conclusion