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6 changes: 3 additions & 3 deletions src/plans/nonlinear_least_squares/nls_general_plan.jl
Original file line number Diff line number Diff line change
Expand Up @@ -203,15 +203,15 @@ For the derivation of the Riemannian case, see [BaranBergmann:2026](@cite).

In order to build a surrogate also for the robustified Levenberg-Marquardt, introduce
``α = 1 - $(_tex(:sqrt, "1 + 2 $(_tex(:frac, "ρ''(p)", "ρ'(p)"))$(_tex(:norm, "F(p)"; index = "2"))^2"))``
and set ``y = $(_tex(:frac, _tex(:sqrt, "ρ'(p)"), "1-α"))F(p)`` and ``$(_tex(:Cal, "L"))(X) = CJ_F^*(p)[F(p)]``
and set ``y = $(_tex(:frac, _tex(:sqrt, "ρ'(p)"), "1-α"))F(p)`` and ``$(_tex(:Cal, "L"))(X) = CJ_F(p)[X]``
with

```math
C = $(_tex(:sqrt, "ρ'(p)"))(I-αP), $(_tex(:qquad)) P = $(_tex(:frac, "F(p)F(p)^" * _tex(:rm, "T"), _tex(:norm, "F(p)"; index = "2") * "^2")),
```

where ``F(p) ∈ ℝ^n`` is the vector of residuals at point ``p ∈ M`` and ``J_F^*(p): ℝ^n → $(_math(:TangentSpace))``
is the adjoint Jacobian.
where ``F(p) ∈ ℝ^n`` is the vector of residuals at point ``p ∈ M`` and ``J_F(p): $(_math(:TangentSpace)) → ℝ^n``
is the Jacobian.
These two can be accessed with [`get_vector_field`](@ref) for ``y`` and [`get_linear_operator`](@ref) for ``$(_tex(:Cal, "L"))``,
respectively.
For technical details on the scaling using ``α``, especially how the `threshold` and `mode`
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