Math Help - find polynomial

1. find polynomial

Hi,

I'm not sure whether this is a suitable problem for this section. Anyway, I have a set of points and I need to find a polynomial.

The points are..
(0,3),(1,10),(2,10),(3,10)....(50,10)

how do I get the polynomial?

2. Re: find polynomial

Originally Posted by mccvinodh
Hi,

I'm not sure whether this is a suitable problem for this section. Anyway, I have a set of points and I need to find a polynomial.

The points are..
(0,3),(1,10),(2,10),(3,10)....(50,10)

how do I get the polynomial?
The best-fit would be the line y = 10.

3. Re: find polynomial

yeah.. but I need to find the value at x = -1. In that y = 10 is not the perfect fir.

4. Re: find polynomial

Originally Posted by mccvinodh
The points are.. (0,3),(1,10),(2,10),(3,10)....(50,10) how do I get the polynomial?
If you mean the polynomial passing through those points, look here:

Lagrange polynomial

5. Re: find polynomial

Originally Posted by FernandoRevilla
If you mean the polynomial passing through those points, look here:

Lagrange polynomial

Yes. I need the one through the points. But the resulting polynomial will be of degree 50. Am I right? Is that the simplest that I can get?

You can express $p(x)=3L_0(x)+10\sum_{i=1}^{50}L_i(x)$ where $L_i(x)=\prod_{j\neq i}\frac{x-j}{i-j}\;(i=0,1,2,\ldots,50)$