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I liked the way he built up the formula, first one point, then two, then three, then the general case. I coded along at home, writing some Common Lisp, structured the same way

https://pastebin.com/GY1YZUGz

In the last five minutes Elliot Nicholson warns that Lagrange Interpolation sometimes wiggles weirdly in between the given points. That is the Runge Spikes thing that I'm interested in.

I thought that I could generate a simple example by running my code. Let the points be (0,0), (1,0), (2,1), (3,0), (4,0). I'm expecting wiggles at the half-integer points.

CL-USER> (funcall (make-poly '((0 . 0)(1 . 0)(2 . 1)(3 . 0)(4 . 0))) 2.5) => 0.703125

That is reasonable

CL-USER> (funcall (make-poly '((0 . 0)(1 . 0)(2 . 1)(3 . 0)(4 . 0))) 3.5) => -0.546875

That little dip is odd, but not too weird.

But if I try interpolating 0 0 0 0 0 1 0 0 0 0 0

CL-USER> (funcall (make-poly '((0 . 0)(1 . 0)(2 . 0)(3 . 0)(4 . 0)
(5 . 1)
(6 . 0)(7 . 0)(8 . 0)(9 . 0)(10 . 0)
)) 0.5)

=> 4.9335175

I get a weird answer at one half. Yah! My first Runge Spike!