This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 ListInterpolation 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. In[1]:= Out[1]= 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}.) In[2]:= ListInterpolation::inhr: Requested order is too high; order has been reduced to {3, 3, 1}. Out[2]= The approximation reproduces the values at each of the points in the table. In[3]:= Out[3]= You can get approximate values at other points. In this case, the interpolation is a fairly good approximation to the function. In[4]:= Out[4]= 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. In[5]:= ListInterpolation::inhr: Requested order is too high; order has been reduced to {2, 2}. Out[5]= Again, the given values are represented by the approximate function. In[6]:= Out[6]= The given derivatives are also represented. In[7]:= Out[7]= Where the derivative was given by Automatic, it is computed automatically by the interpolation. In[8]:= Out[8]= You can also get approximate values at other points. In[9]:= Out[9]= Let's clean up by getting rid of the symbols defined in these examples. In[10]:=