Manuscript Em03-H@8 · Em03-H-v8.tex · section · 91e9e3bd

Exhaustive indexed eigenvalue intervals

Spectral and diagnostic certification › Exhaustive indexed eigenvalue intervals · lines 1673–1686

The full bases named in P8-new can be inputs to this theorem, but its numerical premises remain unestablished here. If centering is used, recompute the centered discrepancy; it is not unchanged when $A$ is only approximately unitary.

For parity-minimum intervals $[a_{+}, b_{+}]$ , $[a_{-}, b_{-}]$ ,

E_{m i n} \in [min (a_{+}, a_{-}), min (b_{+}, b_{-})] .

Strict separation establishes the winning parity; overlap does not establish a tie.

Displayed formulas in this passage

unlabeled · line 1681
$E_{m i n} \in [min (a_{+}, a_{-}), min (b_{+}, b_{-})] .$

Nearby in this section

theorem: Theorem: Full-basis Hermitian certificate