constructs an interpolation of the function values fi, assumed to correspond to x values 1, 2, .


constructs an interpolation of the function values fi corresponding to x values xi.


constructs an interpolation of multidimensional data.


constructs an interpolation that reproduces derivatives as well as function values.


find an interpolation of data at the point x.

Details and Options

  • Interpolation returns an InterpolatingFunction object, which can be used like any other pure function.
  • The interpolating function returned by Interpolation[data] is set up so as to agree with data at every point explicitly specified in data.
  • The function values fi can be real or complex numbers, or arbitrary symbolic expressions.
  • The fi can be lists or arrays of any dimension.
  • The function arguments xi, yi, etc. must be real numbers.
  • Different elements in the data can have different numbers of derivatives specified.
  • For multidimensional data, the n^(th) derivative can be given as a tensor with a structure corresponding to D[f,{{x,y,},n}].
  • Partial derivatives not specified explicitly can be given as Automatic.
  • Interpolation works by fitting polynomial curves between successive data points.
  • The degree of the polynomial curves is specified by the option InterpolationOrder.
  • The default setting is InterpolationOrder->3.
  • You can do linear interpolation by using the setting InterpolationOrder->1.
  • Interpolation[data] generates an InterpolatingFunction object that returns values with the same precision as those in data.
  • Interpolation allows any derivative to be given as Automatic, in which case it will attempt to fill in the necessary information from other derivatives or function values.
  • Interpolation supports a Method option. Possible settings include "Spline" for spline interpolation and "Hermite" for Hermite interpolation.


open allclose all

Basic Examples  (2)

Construct an approximate function that interpolates the data:

Click for copyable input

Apply the function to find interpolated values:

Click for copyable input

Plot the interpolation function:

Click for copyable input

Compare with the original data:

Click for copyable input

Find the interpolated value immediately:

Click for copyable input

Scope  (4)

Generalizations & Extensions  (5)

Options  (5)

Applications  (2)

Properties & Relations  (2)

Possible Issues  (3)

Neat Examples  (1)

See Also

ListInterpolation  FunctionInterpolation  InterpolatingPolynomial  Fit  FindFit  Quantile  Nearest  InterpolatingFunction  Piecewise  BSplineFunction  BezierFunction  ListLinePlot  ListPlot3D  FindSequenceFunction  SequencePredict


Introduced in 1991
| Updated in 2008