I need help building a dynamically evolving matrix based on a polynomial of unknown or user inputted size.

I need help creating an array based on a polynomial of unknown length. Polyval and Poly fit cannot be used.

I need something that would do....

n=length(x);
X=[ones(n,1) x(:)];

% and after 1 iteration

X=[ones(n,1) x(:) x(:).^2];

%and after the 2nd iteration

X=[ones(n,1) x(:) x(:).^2 x(:).^3];

%and after the 3rd iteration

X=[ones(n,1) x(:) x(:).^2 x(:).^3 x(:).^4];

% and so on for n amount of iterations

Answer 1

[Walter Roberson]

xv = x(:);
yv = y(:);
X = [];
deg = 0;
while true
    X = [X, xv.^deg];
    coeffs = X \ yv;
    residue = sum( (polyval(flipud(coeffs), xv) - yv).^2 );
    if residue < tolerance
        break;
    end
end

Answer 2

[Steven Lord]

Take a look at the vander function.

Answer 3

[Terry Poole]

I finally got it last night by using

X=[ones(n,1) x(:)]; for i=2:n X[:,i-1]=X[:,i]+x.^(i+1); end