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

where φi(x), i = 1,2,…,n, are chosen, and the coefficients ci, 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 φi(x)) and the coefficients ci are frequently determined by the least-squares criterion (see approximation theory). Compare interpolation.