Exercise · ZW-RUNGE-PHENOMENON-005 · ★★☆ Intermediate

What happens to the error when the degree increases with equally spaced nodes for \( f(x)=\frac{1}{1+25x^2} \) on \( [-1,1] \)?

Choose one option.

Show answer
  • B. It increases near the endpoints of the interval

Explanation

With equally spaced nodes the error grows near the endpoints as the degree increases. Uniform decrease and vanishing at the endpoints are the opposite of what happens.

Study Numerical methods in ZWMath →

Review the concept: Runge phenomenon

The Runge phenomenon is the oscillatory, divergent behavior of polynomial interpolation errors at high degree when the nodes are equally spaced on an interval.

\[f(x)=\frac{1}{1+25x^2},\quad x\in[-1,1]\]

More practice problems: runge phenomenon

← ZW-RUNGE-PHENOMENON-004 ZW-RUNGE-PHENOMENON-006 →