Interval evaluations

Exact rational entries are not necessary if rigorous enclosures are available. However, a statement that an entry is “numerically small” is not a zero certificate.

For example, if a candidate row $z$ and reference vector $q$ are fixed exactly, and enclosures prove

this proves only nonvanishing of that contraction. To obtain a separator one must also prove exact annihilation of every allowed counterterm response, or give a separately stated approximate-robustness theorem with bounded counterterm coefficients.

Without a bound on the coefficients $c$, a merely small $\Vert zN\Vert$ gives no uniform bound on $|zNc|$.