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Runge's Phenomenon

At first glance, the remainder formula for Lagrange polynomials seems to say that more points are better. In a lot of situations this is the case, but there are some scenarios where something called Runge's phenomenon occurs and you get an oscillating effect at the end points of an interval that makes the results from a polynomial more points worse than one with fewer points. In this lecture, we're going to take a look at Runge's original example and we'll talk about how you can use something called Chebyshev's nodes to bring the larger point approximations back into line with the original function.