is reported by Mosek to be infeasible,. Mosek also issues warnings about near zero elements, The matrix
A has elements as small in magnitude as 3.782361859452318e-18, which is terrible. The maximum magnitude element of A is 2.205118450483101e+02. So the elements of A span 20 orders of magnitude: not good. Or as Gene Golub would have more emphatically labeled it in the Statistical Computing class I took from him: NFG. (I don’t know what he would have labeled the 323 orders of magnitude. The only labels he ever used in class were E, G, NG, NFG).
is reported by Mosek to be dual infeasible. Mosek also issues warnings about near zero elements,
I calculated the unconstrained least squares solution of A*x = b by SVD (which is what
pinv uses) and evaluated the norm of its residual
x_svd = pinv(A)*b;
This appears to show A*x= b is not undetermibned, but is overdetermined, so that A
*x=b does not have an exact solution, and therefore CVX/Mosek’s determination of infeasibility of
A*x == b is correct.
However, that appearance is INCORRECT!! I redid the SVD calculation and norm of residual evaluation using quad precision (34 digits) iin Advanpix Multiprecision Computing Toolbox; the resulting norm = 1.5e-24. So it now appears that Ax = b really is consistent. I then redid the SVD calculation in double quad precision (70 digits) and got norm of residual = 1.59 e-60, reaffirming the consistency of Ax=b.
cond(A) = 9e12 as evaluated in both double precision and quad precision. This is too badly conditioned for Mosek to handle, It s too badly conditioned for double precision SVD to handle accurately. However quad precision can handle it.