Manuscript X-D-ST@1 · X-D-ST.tex · proposition · e0cf8fdb

Proposition: Finite evaluation stability

Finite Enter encoding of supplied limiting evaluations › From the analytic estimate to a declared table · lines 2136–2154 · proof included or linked

X-D-ST@1#prop:evaluations, X-D-ST@1#eq:evaluation-rate

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For any such fixed finite dictionary, there are $M < \infty$ and a positive width bound such that

i max ∣ a_{i, ε} - a_{i, 0} ∣ \leq M ε .

Proof. For each fixed compact support $C_{i}$ , pairing with the fixed smooth solution is a continuous functional on $D_{C_{i}}$ . In particular, a containing compact box gives a bound by a constant times $p_{0}$ . Apply (eq:rate) to each entry and take the maximum over finitely many constants.

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X-D-ST@1#eq:evaluation-rate · line 2140
$i max ∣ a_{i, ε} - a_{i, 0} ∣ \leq M ε .$

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section: From the analytic estimate to a declared table
section: From the analytic estimate to a declared table