LIPs are used for polynomial interpolation. Given points $x_j∈ℝ$ that
are pairwise distinct for $j=0,\cdots k$, we can construct polynomials
$p_j(x)$ that have the following property:
$$
  p_{i}(x_{j}) = δ_{ij}
$$
In particular, given a function $f(x)$, we can construct a polynomial
that agrees with $f$ at any of the points $x_{j}$.  The problem is
that such interpolation might oscillate wildly