Newton Polynomials through Specific Points

[veronicak5678]

I have completed a difference table for 4 points, x0, x1, x2, x3 and found the third degree poly that goes through these four points. Now I need to know how to make the polynomial of second degree that interpolates x0, x2, and x3. Do I just need to remake the table for 3 points, now excluding point x1?

 

[AlephZero]

You could do that, or you could use the basic idea of Lagrange interpolation polynomials:

The polynomial A(x-a)(x-b) is zero when x = a and x = b, and you can make it have any value you want at a third point x = c by choosing the value of A

So write the polynomial in the form
y = A(x-x2)(x-x3) + B(x-x0)(x-x3) + C(x-x0)(x-x2)

If you evaluate it at x = x0, you get
y0 = A(x0-x2)(x0-x3)
which gives you the value of A, and similarly for B and C.

 

[veronicak5678]

Thank you!