How to get polynomial of form ax^2+c

Question

David Ishak 2015-10-29

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回答： Matt J 2015-10-29

I am using MATLAB to fit a curve to data. I have a physics formula of the form y=ax^2+c and I am trying to determine the value of the constant a and c using the data. When I fit a second degree polynomial to the data (using polyfit), MATLAB gives me the constants a b and c of the polynomial in the form of ax^2 + bx + c. Of course, that doesn't help me find a and c for my formula. I need a polynomial of the form ax^2 + 0x + c that fits the data

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Answer 1

Matt J 2015-10-29

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p=polyfit(x.^2,y,1);
a=p(1);
c=p(2);

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Answer 2

Walter Roberson 2015-10-29

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Suppose you have an x vector and a y vector. Then

X = x(:);
Y = y(:);
coeffs = [X.^2, ones(size(X))] \ Y;
a = coeffs(1);
c = coeffs(2);

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Answer 3

Star Strider 2015-10-29

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编辑：Star Strider 2015-10-29

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You have a linear equation, so you can use the mldivide function and an appropriately constructed design matrix to estimate the parameters:

x = 0:9;                                            % Create Data
y = 2 + 5*x.^2 + 0.1*randn(size(x));                % Create Data
B = [ones(size(x(:)))  x(:).^2]\y'                  % Estimate Parameters
B =
     2.0176
     4.9998