You interpolate \( f(x)=\frac{1}{1+25x^2} \) on \( [-1,1] \) with equally spaced nodes. Which statement best describes the behavior when going from degree 5 to degree 15?
Choose one option.
Show answer
A. The error at the endpoints increases, with large oscillations
Raising the degree with equally spaced nodes makes the error grow at the endpoints with large oscillations. The other options assume improvement at the endpoints or exact matching, which do not occur.
The Runge phenomenon is the oscillatory, divergent behavior of polynomial interpolation errors at high degree when the nodes are equally spaced on an interval.