Curve fitting

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 (x_i, y_i), i = 1, . . ., n.

Curve-fitting procedures include interpolation, in which case f(x_i) = y_i 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(x_i) and y_i 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.

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