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Here's some Clojure code I wrote for the Emmy computer algebra system that implements polynomial interpolation with a few different algorithms described in Numerical Recipes:
https://github.com/mentat-collective/emmy/blob/main/src/emmy...
I discovered while writing this that I could express each of these algorithms as folds that consumed a stream of points, accumulating a progressively higher order polynomial.
Here's the same sort of thing but for rational function interpolation: https://github.com/mentat-collective/emmy/blob/main/src/emmy...