Numerical Analysis/Lagrange example

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We'll find the interpolating polynomial passing through the points , , , using the Lagrange method.

We first use the formula to write the following:

After some simplification, we get:

And our answer:

.

Adding a point[edit]

Now we'll add a point to our data set, and find a new interpolating polynomial. Let us add the point to our set. Starting over with the Lagrange formula, we write:

Simplifying, we get:

And our polynomial is:

.