# Curve fitting

From AMS Glossary

## 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.