Manuscript IX-C-ST@1 · IX-C-ST.tex · section · 892f50c4

Finite evaluation records and a normed comparison

Shared finite clock, certificates, and regular transport › Finite evaluation records and a normed comparison · lines 840–866

Back to manuscript

For a supplied complex coefficient evaluation $z_{k i}$ , one may install

v_{k i} = clip (Re z_{k i} / M_{k i}), M_{k i} > 0, clip (u) = max {- 1, min {1, u}} .

If $∣ z_{k i} - z_{k i} ∣ \leq E_{k i}$ , then

d_{⋄} (I_{v}, I_{v}) \leq min {1, k i max \frac{E _{k i}}{2 M _{k i}}} .

For the parent numerical coefficient, an enclosure can use

E_{ε} \leq e_{T} + ∣ lo g ((μ ε)^{- 1}) ∣ e_{r} + C ε (1 + ∣ lo g ε ∣) p_{A, 64 + d} (Φ),

when $e_{T}, e_{r}$ are supplied enclosures of the regular pairing and residue pairing. This is a triangle-inequality consequence of Lemma lem:transfer. No executed quadrature, field acquisition, charge measurement, or residue measurement is asserted.

Displayed formulas in this passage

unlabeled · line 844
$v_{k i} = clip (Re z_{k i} / M_{k i}), M_{k i} > 0, clip (u) = max {- 1, min {1, u}} .$
unlabeled · line 850
$d_{⋄} (I_{v}, I_{v}) \leq min {1, k i max \frac{E _{k i}}{2 M _{k i}}} .$
unlabeled · line 855
$E_{ε} \leq e_{T} + ∣ lo g ((μ ε)^{- 1}) ∣ e_{r} + C ε (1 + ∣ lo g ε ∣) p_{A, 64 + d} (Φ),$

Finite evaluation records and a normed comparison

Displayed formulas in this passage

Nearby in this section