Curve fitting

From Glossary of Meteorology

curve fitting

The derivation of an analytic function f(x) with its graph y = f(x) passing through or approximately through a finite set of data points (xi, yi), i = 1, . . ., n.

Curve-fitting procedures include interpolation, in which case f(xi) = yi for each data point, and the least squares method, in which case the derived function minimizes the sum of the squares of the differences between f(xi) and yi over all the data points. The functions used in curve fitting are usually polynomials. In least squares methods, a single polynomial of low degree typically is used over the entire range of x spanned by the data; in interpolation procedures, a separate polynomial typically is defined over each subinterval and the polynomial pieces connected through imposition of certain continuity conditions.
See spline function.