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

Question

Terry Poole 2019-4-22

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回答： Terry Poole 2019-4-22

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

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Answer 1

Walter Roberson 2019-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/457722-i-need-help-building-a-dynamically-evolving-matrix-based-on-a-polynomial-of-unknown-or-user-inputted#answer_371613

编辑：Walter Roberson 2019-4-22

在 MATLAB Online 中打开

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