I need help figuring out the mistake in my function approximation
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Matlab1
el 26 de Oct. de 2023
Comentada: Matlab1
el 26 de Oct. de 2023
I am doing function approximation but i'm not getting a smooth function at all. I've tried least squares method and backslash for the same question. Could someone please point out my mistake and help me? Thank you.
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the cyclist
el 26 de Oct. de 2023
Your 5th-degree polynomial is smooth (but not unique, because you only have 4 data points). You just don't plot on a fine enough grid to see it. Here, I plot just your 2nd and 5th-order polynomials, on a finer grid.
x = [0.1 0.3 0.4 0.6 0.9];
y = [0 2.2 1 0.6 3.7];
x0 = 0 : 0.02 : 0.9;
for m = [2 5]
P = polyfit(x,y,m);
yaprox = polyval(P,x);
yaprox0 = polyval(P,x0);
figure
hold on
plot(x,y,'o','MarkerSize',8);
plot(x0,yaprox0,'ro-','MarkerSize',2);
xlabel('x')
ylabel('y')
legend('data','fit')
end
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John D'Errico
el 26 de Oct. de 2023
Editada: John D'Errico
el 26 de Oct. de 2023
Avoid the use of the normal equations as you used, i.e., this crapola that you called the least squares method. Backslash is just as much a least squares method!
% A = [sum(x.^2) sum(x.^3)
% sum(x.^3) sum(x.^4)];
% b = [sum(y.*x);sum(y.*x.^2)];
%
% % solution of the system
% c = inv(A)*b;
Properly solve for the coefficients using backslash.
x = [0.1 0.4 0.9 1.6 1.8]';
y = [0.4 1.0 1.8 4.1 5.5]';
Your model is: f(x) = c1x + c2x^2
A = [x,x.^2];
C12 = A\y;
plot(x,y,'o');
hold on
yfun = @(X) C12(1)*X + C12(2)*X.^2;
fplot(yfun,[min(x),max(x)])
Note my use of fplot there. Your evaluation of the points on the curve
% xx = x(1):0.1:x(end);
was a bad idea. Why? How many points did it generate? LOOK CAREFULLY! Just because 0.1 seems like a small number, IS IT REALLY????? What is x again?
x = [0.1 0.4 0.9 1.6 1.8]';
Alternatively, you might have used linspace to generate that vector. I would suggest your real problem was in just the use of a stride of 0.1 between points to evaluate the curve at.
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