Editing Extrapolation (section)

===Polynomial===
[[File:Lagrange polynomials for continuations of sequence 1,2,3.gif|thumb|right|Lagrange extrapolations of the sequence 1,2,3. Extrapolating by 4 leads to a polynomial of minimal degree ({{color|#006060|cyan}} line).]]
A polynomial curve can be created through the entire known data or just near the end (two points for linear extrapolation, three points for quadratic extrapolation, etc.).  The resulting curve can then be extended beyond the end of the known data.  Polynomial extrapolation is typically done by means of  [[Lagrange interpolation]] or using Newton's method of [[finite differences]] to create a [[Newton series]] that fits the data. The resulting polynomial may be used to extrapolate the data.

High-order polynomial extrapolation must be used with due care. For the example data set and problem in the figure above, anything above order 1 (linear extrapolation) will possibly yield unusable values; an error estimate of the extrapolated value will grow with the degree of the polynomial extrapolation. This is related to [[Runge's phenomenon]].