How to fit a polynom to known points without polyfit

Hello there,

I'm new to matlab and I was given the task to fit a polynom to a set of known points without using polyfit by my teacher. I've been dabbling around for hours now and I just can not figure it out.

Here are the given Points:

(-3|0) (-2|0) (-1|0) (0|0) (2|0) (2.5|0)

And I was given the Point (1|1)

I figured out how to fit the polynom to the y=0 points but I can not figure out how to fit it to the (1|1)

Here is my code so far (without the plot)

x = linspace(-4,3,701)' ; % x-Achse

NSx = [ -3 -2 -1 0 2 2.5 ]'; % Bekannte Werte x
% 
% y1 = 0;
% 
ko = 0;

p = poly(NSx);

y1 = polyval(p,x);

Can somebody please help me solve this issue?

[David Goodmanson]

Hi Valentn,

If p(x) is a polynomial with a certain set of roots, then p(x)*(x-a) is a polynomial one degree higher that still has the same roots as p(x), correct? (plus one more). You can use this fact to help get a fit to (1,1).

Answer 1

[Walter Roberson]

http://bueler.github.io/M310F11/polybasics.pdf

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

[Valentin Messerle]

Thank you for this ressource. I'll try this right now.

[Valentin Messerle]

This was very helpful. Got it now. Thanks a lot