Fixed Point Iteration: Examples, Analysis, and the Banach Fixed Point Theorem

We explore fixed point iteration, the process of repeatedly applying a function to itself. This is similar to pressing a function button on a calculator over and over again. Sometimes, this process will converge to a fixed point, called an attractor. Sometimes, it will not. We explore various functions like cosine and sine and observe their behavior using graphs, analyses and short Haskell programs. We also introduce the Banach Fixed Point Theorem which allows to more formally define when and where a function will converge to a fixed point.
For more information, we recommend starting with these articles.
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You're welcome! Glad this video was of help to you 😺. A follow-up in this series is coming soon

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Your welcome. And good luck on your exam!

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[@CatSynthTV]

Thanks! More on the way 😺

[@davidemasi__]

Very nice video, could you please explain what happens between the 2 points in the last case?

[@CatSynthTV]

Thanks! Between those points, it can bounce around periodically or chaotically. I’m working on a whole video about that; I expect to drop it this month 😺

[@davidemasi__]

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