How to calculate polynomial coefficient in this case?

Hollo. I want to formulate P(x) as a polynomial function,

So: P(x) = C1 + C2 * X + C3 * X^2 + C4 * X^3 + C5 * X^4 ...... + Cn * X^n-1.

How do I do to obtain C1, C2, C3, C4, ........... Cn ?

Knowing that (for example):

P(1)=1

P(2)=3

P(3)=9

. . . . P(10)=1200... etc.

Thanks!

Answer 1

[Matt J]

Use POLYFIT

[Matt J]

However, a 10-th order polynomial, like in your example, could be hard to fit.

Answer 2

[Roger Stafford]

Another possibility is to use the Lagrange formulation of the polynomial in symbolic form and then use the Symbolic Toolbox 'collect' function on that expression. Or better still use 'coeffs'. See

http://en.wikipedia.org/wiki/Lagrange_polynomial

Note: With ten points the Lagrange polynomial will admittedly be tedious to construct, but you can do it.