Description:

Lagrange interpolation functions.

What can be modified:

• order of interpolating polynom,
• number of elements,
• position of nodes,
• nodal values.

Notice:

• approximation is continuous and smooth (derivatives of all orders are continuous) within one element, while it is only continuous (it may "kink") between elements.
• interpolating functions has value equal to 1 at exacly one node, while it has value equal to 0 in all other nodes ("Kronecker delta property"),
• sum of values of interpolating functions in arbitrary point is equal to 1.
• change of nodal value affect the approximation only on element(s) which the node belongs to.