Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
This method improves finite-step optimization for nonlinear least-squares by using Riemann Normal Coordinates (RNC) to incorporate higher-order geometric corrections into the Levenberg-Marquardt algorithm. It reformulates the geodesic equation as a residual condition, allowing updates to follow the true curved geometry rather than straight lines, leading to faster convergence and better accuracy.