This paper delves into the accuracy of the Gauss-Newton curvature within ridge-regularized nonlinear least squares. It establishes that under specific conditions of local regularity and persistent level-set curvature, two distinct curvature regimes uniformly coexist. The research proves the existence of global minimizers and provides bounds for their relative Hessian error, while also identifying points within the same low-cost set that exhibit an indefinite Hessian with a higher relative error. The study further details how a positive ridge cap functions across various perturbations and demonstrates that these neighborhoods remain stable as the ridge weight approaches zero. A pointwise certificate is introduced to manage the Hessian correction components, and a sharp relative-error bound is derived for varying prediction maps and ridges. Additionally, the paper presents analytic examples illustrating the influence of output alignment, curvature orientation, and persistence, alongside a structural result confirming full Jacobian row rank in low-cost sets and exact interpolation near rank-deficient references. AI
RANK_REASON The item is a research paper detailing mathematical and algorithmic findings. [lever_c_demoted from research: ic=1 ai=0.1]
Read on Hugging Face Daily Papers →
- Gauss–Newton algorithm
- Hessian error
- Hessians Motorcycle Club
- Jacobian matrix
- level-set curvature
- Nonlinear least-squares data fitting in Excel spreadsheets.
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