Matlab - Least squares approximation of f(x) = e^x

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.