A means by which a table of values f(x₀), f(x₁),…, f(x_m) at the distinct points x₁, x₂,…, x_m, can be approximated (represented) by a function, say

where ϕ‎_i(x), i = 1,2,…,n, are chosen, and the coefficients c_i, i = 1,2,…,n, are to be determined. Typically m > n. The objective is to choose a fit that reduces the effect of random errors in the data combined with producing a curve that is smooth (no rapid changes or oscillations) between the data points. This is generally referred to as smoothing. The smoothing is often achieved by using low-degree polynomials (with suitable ϕ‎_i(x) and the coefficients c_i are frequently determined by the least-squares criterion (see approximation theory). Compare interpolation.