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ListInterpolation

ListInterpolation[array] constructs an InterpolatingFunction object that 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 that returns values with the same precision as those in {array, domain}.
• See also:
Interpolation, ListContourPlot.

Examples

Using InstantCalculators

Here are the InstantCalculators for the ListInterpolation function. Enter the parameters for your calculation and click Calculate to see the result.

Evaluate the function at a point.

Entering Commands Directly

You can paste a template for this command via the Text Input button on the ListInterpolation Function Controller.

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.

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.

Clear the variable definitions.



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