The Lagrangeian interpolating polynomial for a set of dataOriginally Posted byBanderHM

is a polynomial of degree (the number of data points) which passes exactly

through each of the data points. It can be written explicitly in terms of the

data as shown below:

Consider the polynomials:

,

This equals at , and equals when .

Hence:

is a polynomial such that .

This is the Lagrange interpolating polynomial for the data .

There is one more thing to say about Lagrangian interpolation, and that is

it is of more importance to theory than practice. If you actualy want to

interpolate on real data there are almost always better ways of doing so

than Lagrangian interpolation.

RonL