Help plotting interpolation ploynomial.

Hi, I was asked to plot psi_n(x) = (x-x_0)(x-x_1)...(x-x_n) for n = 3,7,10,17 evenly distributed nodes in [-5,5] with resolution 0.01. Below is my code:

x=-5:0.01:5;
n=[3 7 10 17];
for j=1:4
    node=-5;
    psi=1;
    while (node <= 5)
        psi=psi.*(x-node);
        node=node + 10/n(j);
    end
    subplot(2,2,j);
    plot(psi)
    hold on
end

Which doesn't quite yield the desired output. Or does it? In any case, it doesn't seem to match what I am getting via using Wolfram. My question is why and, of course, how may I correct it? I'd sincerely appreciate your assistance. Thanks in advance!

[Simon]

Hi!

What is x_0, x_1, ...?

[Yuval]

The nodes. x_0 is x index zero.

Answer 1

[Matt J]

node=linspace(-5,5,n);

p=poly(node);

f=@(z) polyval(p,z);

x=-5:0.01:5;
plot(x,f(x));

[Yuval]

Hi Matt, Thank you for your reply. Would you kindly care to explain your code? Also, did you realise I wasn't trying to actually plot the interpolation polynomial but merely the product function psi? I just tried using your code and it yielded the following error message: ??? Error using ==> mrdivide Matrix dimensions must agree.

Error in ==> linspace at 22 y = [d1+(0:n-2)*(d2-d1)/(floor(n)-1) d2]; Error in ==> psierror at 2 node=linspace(-5,5,n);

[Matt J]

Also, did you realise I wasn't trying to actually plot the interpolation polynomial but merely the product function psi?

From your description of psi_n(x), it appears to be a polynomial function of x with roots at the nodes x_0,...,x_n. That is what I have given you.

I just tried using your code and it yielded the following error message:

In my code, n is assumed to be a scalar. It runs error-free for me when this is the case.

[Victor McNstein]

Hello Matt. How does on combine your code with Yuval's initial work, for better results?

[Matt J]

I do not see what Yuval thought was incomplete about my code. I think my code already fulfills the entire task.