Construct an approximate function that interpolates the data:

Apply the function to find interpolated values:

Plot the interpolation function:

Compare with the original data:

Construct an approximate function with the x values equally spaced on the interval :

Apply the function to find interpolated values:

Plot the interpolation function with the original data:

Construct an approximate function that interpolates the values from an array of values:

Plot the function with the original data:

Interpolate between points at arbitrary x values:

The x values may be included in the data directly:

Create data with Table :

Form the interpolation:

Plot the interpolated function:

Create a list of multidimensional data:

Create an approximate interpolating function:

Plot the interpolating function:

Create data including derivative values:

Construct an interpolation:

Plot the interpolation:

Create 2D data that includes a gradient vector at each point:

Compare with data that does not include gradients:

Also include tensors of second derivatives:

The interpolating function always goes through the data points:

Find the integral of an interpolating function:

Plot the interpolating function and its integral:

Find a root of the integral:

Beyond the domain defined by the original data extrapolation is used:

A plot shows the inaccuracy of extrapolation:

With the default choice of order, at least 4 points are needed in each dimension:

With a lower order, fewer points are needed:

The interpolation function will always be continuous, but may not be differentiable:

If derivatives are specified, the interpolation function will have a continuous ^(th) derivative: