Runge's Phenomenon

number of points

5

sampling method

equally spaced

Chebyshev points

Chebyshev sample points

Runge's phenomenon illustrates the error that can occur when constructing a polynomial interpolant of high degree. The function to be interpolated,

y=

1

1+25

2

x

, is shown in orange, the interpolating polynomial in blue, and the data points in red. The difference between the interpolant and the function is shown below.