Computing the Newton Step: GD as a Matrix-Free Way

This lecture covers matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds. It discusses the paradigm of Hessf(x) as an operator, the Newton step minimization, and the use of gradient descent on TxM. The instructor explains the optimization algorithm on mx, the gradient descent process, and the iterative steps to minimize g(v) on TxM. The lecture concludes with the implementation of gradient descent to minimize g(v) on TxM, emphasizing the iterative process and convergence criteria.