Output doesn't seem to be correct

Question

Sherman Ng 2022-3-15

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https://ww2.mathworks.cn/matlabcentral/answers/1671794-output-doesn-t-seem-to-be-correct

回答： Gyan Vaibhav 2023-11-16

Hi so this is the polynomial question that I've been stuck on for a while, this is what I have so far but apparently my output is not correct.

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Torsten 2022-3-15

Yes, you only did it for degree 9.

Make a loop to get coefficients and values for the other degrees.

Sherman Ng 2022-3-15

编辑：Walter Roberson 2022-3-15

在 MATLAB Online 中打开

So something like this?

n=9
c = zeros(n,n+1); 
for k = 1:n
    syms x y
    z(k) = (x+y)^k;
    coeff = coeffs(z(k));
    c(k,1:k+1) = double(coeff); 
end

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Answer 1

Gyan Vaibhav 2023-11-16

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https://ww2.mathworks.cn/matlabcentral/answers/1671794-output-doesn-t-seem-to-be-correct#answer_1353782

在 MATLAB Online 中打开

Hi Sherman,

I understand that you are trying to evaluate the coefficients for a polynomial of degree 9 that passes through the mentioned points. You also want to calculate the values of the polynomial at specific points.

This can be achieved using the “polyfit” function to fit the given values to a polynomial of the desired degree. This function fits a polynomial to the given data points using least squares regression. Afterwards, you can evaluate the polynomial at different points using the “polyval” function.

It can be done as follows:

% Given data points
x = [0, 0.1111, 0.2222, 0.3333, 0.4444, 0.5556, 0.6667, 0.7778, 0.8889, 1];
y = [0, 6.988, 5.1826, -3.1445, -7.5146, -2.4209, 5.7187, 6.6621, -0.7779, -7.2391];
% Degree of the polynomial
degree = 9;
% Fit the polynomial using polyfit
coefficients = polyfit(x, y, degree);
% Evaluate the polynomial at specified x-values
x_values = 0:0.01:1;
y_values = polyval(coefficients, x_values);
% Display the coefficients vector
coefficients_vector = coefficients'
% Display the x-y values as two rows of a matrix
xy_matrix = [x_values; y_values];