Fix LM surrogate operator documentation#621
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* Fix a few typos in the random walk solver example. * Initial setup of Gradient Sampling. * Setup the boiler plate code for the high-level interface and create the documentation page. * Sketch the algorithm further. * add a bit of documentation. * Documentation and show/print for the gradient sampling state * Setup a first example and fix the firrst few bugs. * Add Changelog entry. * add Ole Gunnar to the about.md * Update Hajgs link on the about page. * Start testing. * bump version. * Apply suggestions from code review --------- Co-authored-by: Ole Gunnar Røsholt Hovland <73483154+elorannug@users.noreply.github.com>
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This PR fixes a small documentation typo in the Levenberg–Marquardt linear surrogate description based on the very reference https://arxiv.org/pdf/2606.23560.
The surrogate operator is defined as$\mathcal L : T_pM \to \mathbb R^n,$ so it should use the Jacobian action $\mathcal L(X) = C J_F(p)[X],$ rather than the adjoint Jacobian applied to the residual. The latter lives in the tangent space and is dimensionally inconsistent with the definition of $\mathcal L$ . I also updated the following explanatory sentence to describe $J_F(p)$ as the Jacobian linear operator.