6
As Federico has mentioned, you probably don't want to deprive yourself of the learning experience. I'll just give you a small nudge in the right direction.
You will never be able to store $A$. You also won't be able to store $(A+uv^T)^{-1}$. However, you don't really need to. You can easily write down a formula for each of the entries in $A$.
Instead of ...
4
Sounds like you want to omit the use of a MATLAB toolkit/Octave package. Of course you can build the bode diagram from scratch:
% transfert function as anonymous function
h = @(s)(1)./(2*s.^2+3*s+4);
% frequency vector
w = 2*pi*logspace(-2,2,1000);
% magnitude & phase estimation
mag = abs(h(1j*w));
magDB = 20*log10(mag);
phaseDeg = rad2deg(angle(h(1j*w))...
2
Pseudoinverse can be computed using the SVD $A = USV^\top$ by:
$$
A^+ = V\Sigma^+ U^\top
$$
where $\Sigma^+$ is formed from $\Sigma$ by taking the reciprocal of all the non-zero elements. With that in mind, you could use MATLAB's svds function as follows:
[U,S,V] = svds(A,k);
Ainv = V*diag(1./diag(S))*U';
Here k refers to the rank and svds computes only a ...
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