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Equally spaced interpolation constructs an interpolant from data at nodes $x_j=a+jh$. It is convenient when measurements or a computational grid already have uniform spacing. The degree-at-most-$n$ polynomial interpolant through $n+1$ distinct nodes is unique, but uniqueness does not imply good approximation as $n$ increases.

For $f(x)=1/(1+25x^2)$ on $[-1,1]$, high-degree polynomial interpolation at equally spaced nodes exhibits Runge's phenomenon near the endpoints. Chebyshev nodes reduce that endpoint instability by clustering there; piecewise spline interpolation offers another alternative. The data locations and the degree must therefore be treated as approximation choices, rather than assuming that more uniformly spaced data always improve a global polynomial.