Manuscript Oai282-A@1 · Oai282-A.tex · section · 5b6134ec

A complete finite correction test

The finite local-Ward certificate › A complete finite correction test · lines 985–1003

Suppose all correction freedom allowed for this finite task has been independently parameterized by a real affine family

W (c) = W_{0} + α = 1 \sum^{p} c_{α} H_{α}, c_{α} \in R .

Reality preserves the specified Hermitian convention. Additional exact linear admissibility conditions may first be absorbed into a parameterization of the permitted affine space.

Let $E$ evaluate all named matrix residuals, splitting complex entries into real and imaginary parts. Write

w_{0} = E (W_{0}) \in R^{m}, N_{:, α} = E (H_{α}) .

Displayed formulas in this passage

unlabeled · line 989
$W (c) = W_{0} + α = 1 \sum^{p} c_{α} H_{α}, c_{α} \in R .$
unlabeled · line 999
$w_{0} = E (W_{0}) \in R^{m}, N_{:, α} = E (H_{α}) .$

Nearby in this section

proposition: Proposition: Exact finite correction feasibility
section: A complete finite correction test