Coalescing nodes
Pair-indexed interpolation rows are arranged so that three principal Lagrange coefficients approach A, -A, and 1. The selected row therefore has a large Lebesgue function.
Both questions are answered affirmatively.
There exists a triangular array of distinct interpolation nodes in [-1, 1] whose Lebesgue functions λn satisfy
lim supn → ∞ λn(x) = ∞for every x ∈ [-1, 1],
while for every continuous function f there is a point xf ∈ [-1, 1] such that
Lnf(xf) → f(xf).
The second statement holds at the same point where the Lebesgue functions are unbounded along a subsequence.