```
cvx_begin
variable x(4096,1)
A*x==b
cvx_end
```

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).

```
cvx_begin
variable x(4096,1)
minimize(norm(A*x-b))
cvx_end
```

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;
norm(A*x_svd-b)
```

ans =

0.025485457980114

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 A*x = 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 A*x=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.