If the interpolation error is written as \( \frac{f^{(n+1)}(\xi)}{(n+1)!}\prod(x-x_i) \), what happens when switching from equally spaced nodes to Chebyshev nodes?
Choose one option.
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D. The nodal product is strongly reduced near the endpoints
Chebyshev nodes reduce the nodal product near the endpoints and so lower the error. The derivative does not vanish, the factorial does not grow, and the error still depends on the nodes.
The Runge phenomenon is the oscillatory, divergent behavior of polynomial interpolation errors at high degree when the nodes are equally spaced on an interval.