Hello,

I'm having some trouble with finding the least squares approximation (with given n) of in [−1, 1] using matlab. The approximation should be of form .

My Matlab code:

Code:

function z = leastsq(n)

**Plot **

Code:

x = (-1.5:0.001:1.5);
y = exp(x);
plot(x, y);
xlim([-1.5 1.5])

**Integral of **

Code:

matrixf = zeros(n,1);
for (grade = 0:n)
matrixf(grade+1,1) = quad(@(x) exp(x)*exp(grade),-1,1);
end

__Problem:__ matrix with coefficients of

Code:

for (count = 0:n)
if (count == 0 && mod((1+gradex),2) ~= 0)
matrixa(gradex+1, 1) = 2/(count+1+gradex);
elseif (count ~= 0)
matrixa(gradex+1, count+1) = quad(@(x) exp((count)*x)*exp(gradex),-1,1);
end
end

The code I used here succesfully calculates the coefficients for . I can't find how to make it work for ...

The next step would be to calculate the coefficients to :

Code:

coef = matrixa\matrixf

Finally the function should be constructed and plotted.

Any hints or tips would be greatly appreciated.