This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# Interpolation

 Interpolation[{f1, f2, ...}]constructs an interpolation of the function values fi, assumed to correspond to x values , , ... . Interpolation[{{x1, f1}, {x2, f2}, ...}]constructs an interpolation of the function values fi corresponding to x values xi. Interpolation[{{{x1, y1, ...}, f1}, {{x2, y2, ...}, f2}, ...}]constructs an interpolation of multidimensional data. Interpolation[{{{x1, ...}, f1, df1, ...}, ...}]constructs an interpolation that reproduces derivatives as well as function values.
• 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 derivative can be given as a tensor with a structure corresponding to D[f, {{x, y, ...}, n}].
• Interpolation works by fitting polynomial curves between successive data points.
• The default setting is .
• You can do linear interpolation by using the setting .
• 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.
 Scope   (3)
 Options   (4)
 Applications   (2)