Editing Polynomial interpolation (section)

==Related concepts==
[[Runge's phenomenon]] shows that for high values of {{mvar|n}}, the interpolation polynomial may oscillate wildly between the data points. This problem is commonly resolved by the use of [[spline interpolation]]. Here, the interpolant is not a polynomial but a [[spline (mathematics)|spline]]: a chain of several polynomials of a lower degree.

Interpolation of [[periodic function]]s by [[harmonic analysis|harmonic]] functions is accomplished by [[Fourier transform]]. This can be seen as a form of polynomial interpolation with harmonic base functions, see [[trigonometric interpolation]] and [[trigonometric polynomial]].

[[Hermite interpolation]] problems are those where not only the values of the polynomial ''p'' at the nodes are given, but also all derivatives up to a given order. This turns out to be equivalent to a system of simultaneous polynomial congruences, and may be solved by means of the [[Chinese remainder theorem]] for polynomials. [[Birkhoff interpolation]] is a further generalization where only derivatives of some orders are prescribed, not necessarily all orders from 0 to a ''k''.

[[Collocation method]]s for the solution of differential and integral equations are based on polynomial interpolation.

The technique of [[rational function modeling]] is a generalization that considers ratios of polynomial functions.

At last, [[multivariate interpolation]] for higher dimensions.