Editing Spline interpolation (section)

{{short description|Mathematical method}}
{{broader|Spline (mathematics)}}
{{more footnotes|date=July 2021}}
In the [[mathematics|mathematical]] field of [[numerical analysis]], '''spline interpolation''' is a form of [[interpolation]] where the interpolant is a special type of [[piecewise]] [[polynomial]] called a [[spline (mathematics)|spline]]. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-nine polynomial to all of them. Spline interpolation is often preferred over [[polynomial interpolation]] because the [[interpolation error]] can be made small even when using low-degree polynomials for the spline.<ref>{{cite journal |last1=Hall |first1=Charles A. |last2=Meyer |first2=Weston W. |title=Optimal Error Bounds for Cubic Spline Interpolation |journal=Journal of Approximation Theory |date=1976 |volume=16 |issue=2 |pages=105–122 |doi=10.1016/0021-9045(76)90040-X |doi-access=free}}</ref> Spline interpolation also avoids the problem of [[Runge's phenomenon]], in which oscillation can occur between points when interpolating using high-degree polynomials.