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  • ListInterpolation[ array ] constructs an InterpolatingFunction object which represents an approximate function that interpolates the array of values given.
  • ListInterpolation[ array , xmin , xmax , ymin , ymax , ... ] specifies the domain of the grid from which the values in array are assumed to come.
  • You can replace xmin , xmax etc. by explicit lists of positions for grid lines. The grid lines are otherwise assumed to be equally spaced.
  • ListInterpolation[ array ] assumes grid lines at integer positions in each direction.
  • array can be an array in any number of dimensions, corresponding to a list with any number of levels of nesting.
  • ListInterpolation[ array , domain ] generates an InterpolatingFunction object which returns values with the same precision as those in array , domain .
  • See notes for Interpolation.
  • See the Mathematica book: Section 3.8.2.
  • See also: FunctionInterpolation, ListContourPlot.

    Further Examples

    ListInterpolation is similar to Interpolation, but provides a more convenient interface for data that does not include coordinates and for multidimensional data.
    Here is a table of values of a function on a regular three dimensional grid.



    This constructs an approximate function that represents these values. There is not enough data in the z direction (only z = 0 and z = 1) for a higher order approximation, so the order in that direction is reduced automatically. (Reducing the order can be done manually; in this case it would have been by specifying the option InterpolationOrder->{3,3,1}.)


    ListInterpolation::inhr: Requested order is too high; order has been reduced to {3, 3, 1}.


    The approximation reproduces the values at each of the points in the table.



    You can get approximate values at other points. In this case, the interpolation is a fairly good approximation to the function.



    Here values and derivatives specified at the points , , and . There is not enough data to construct a third order (cubic) polynomial in either the x or the y direction, so the (default) interpolation order of is reduced automatically.


    ListInterpolation::inhr: Requested order is too high; order has been reduced to {2, 2}.


    Again, the given values are represented by the approximate function.



    The given derivatives are also represented.



    Where the derivative was given by Automatic, it is computed automatically by the interpolation.



    You can also get approximate values at other points.



    Let's clean up by getting rid of the symbols defined in these examples.