Add Traub's algorithm as solver option for Newton-style implementations

[Copilot]

Implements Traub's method, a third-order root-finding algorithm, as an alternative to Newton's method throughout the package. Traub's method achieves cubic convergence with only two function evaluations per iteration by reusing the Jacobian, making it more efficient when Jacobian computation is expensive.

Changes

• src/algorithms/nonlinear_solver.jl: Added traub() function with identical interface to newton()

  • Two-step iteration: y = x - f(x)/f'(x), then x_new = y - f(y)/f'(x)
  • Handles sparse/dense matrices, bound constraints, convergence tracking

• src/filter/find_shocks.jl: Added find_shocks(::Val{:Traub}, ...) implementations

  • Second-order variant for 𝐒ⁱ²ᵉ problems
  • Third-order variant for 𝐒ⁱ³ᵉ problems
  • Follows LagrangeNewton pattern with Traub's two-step approach

Usage

filter_data_with_model(
    model,
    data,
    Val(:pruned_second_order),
    Val(:inversion);
    filter_algorithm = :Traub,  # Previously only :LagrangeNewton available
    opts = opts
)

Convergence characteristics:

• Newton: 2nd order, 1 function + 1 Jacobian eval
• Traub: 3rd order, 2 functions + 1 Jacobian eval

Original prompt

implement Traubs algorithm as an option for any newton and lageange newton style implementation in the package

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