Rule of Thumb.

    The "best a priori choice" of interpolation nodes for the interval [-1,1] are the n+1 nodes that are zeros of the Chebyshev polynomial  .  

Here is a visual analysis of equally spaced nodes verses Chebyshev nodes on [-1,1], and their affect on the magnitude of Q(x) in the remainder term  .  

Exploration 5.

Observation.  The magnitude of Q(x) is less when the Chebyshev nodes are used and larger when equally spaced notes are used.  This becomes more pronounced when the degree is larger.

Are you convinced that using the Chebyshev nodes on [-1,1], will decrease the magnitude of the term Q(x) in the remainder term  ?  

(c) John H. Mathews 2004