Descent line search scheme using Gers̆gorin circle theorem

In the context of the minimization of a real function, we propose a line search scheme that involves a new positive definite modification of the Hessian. In this framework, a safeguard based on Gers̆gorin Circle's theorem provides an approximation of the Hessian that improves with iteration count. Convergence analysis of the scheme is validated by numerical experiments.