Mercurial > repos > pointsource_algs / file comparison
comparison: src/forward_model.rs
src/forward_model.rs
- branch
- dev
- changeset 63
- 7a8a55fd41c0
- parent 61
- 4f468d35fa29
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| 61:4f468d35fa29 | 63:7a8a55fd41c0 |
|---|---|
| 46 /// Curvature error control: helper bounds for (4.2d), (5.2a), (5.2b), (5.15a), and (5.16a). | 46 /// Curvature error control: helper bounds for (4.2d), (5.2a), (5.2b), (5.15a), and (5.16a). |
| 47 /// | 47 /// |
| 48 /// Based on Lemma 5.11 and Example 5.12, the helper bound for (5.15a) and (5.16a) is (3.8). | 48 /// Based on Lemma 5.11 and Example 5.12, the helper bound for (5.15a) and (5.16a) is (3.8). |
| 49 /// Thus, subject to `guess` being correct, returns factor $(ℓ_F, Θ²)$ such that | 49 /// Thus, subject to `guess` being correct, returns factor $(ℓ_F, Θ²)$ such that |
| 50 /// $B_{F'(μ)} dγ ≤ ℓ_F c_2$ and $⟨F'(μ+Δ)-F'(μ)|Δ⟩ ≤ Θ²|γ|(c_2)$, where $Δ=(π_♯^1-π_♯^0)γ$. | 50 /// $B_{F'(μ)} dγ ≤ ℓ_F c_2$ and $⟨F'(μ+Δ)-F'(μ)|Δ⟩ ≤ Θ²|γ|(c_2)$, where $Δ=(π_♯^1-π_♯^0)γ$. |
| 51 /// The latter is the firm transport Lipshitz property of (3.8b) and Lemma 5.11. | |
| 51 /// | 52 /// |
| 52 /// This trait is supposed to be implemented by the data term $F$, in the basic case a | 53 /// This trait is supposed to be implemented by the data term $F$, in the basic case a |
| 53 /// [`Mapping`] from [`RNDM<N, F>`] to a [`Float`] `F`. | 54 /// [`Mapping`] from [`RNDM<N, F>`] to a [`Float`] `F`. |
| 54 /// The generic implementation for operators that satisfy [`BasicCurvatureBoundEstimates`] | 55 /// The generic implementation for operators that satisfy [`BasicCurvatureBoundEstimates`] |
| 55 /// uses Remark 5.15 and Example 5.16 for (4.2d) and (5.2a), and (5.2b); | 56 /// uses Remark 5.15 and Example 5.16 for (4.2d) and (5.2a), and (5.2b); |
