 Newton step

A Newton step for Newton's method in optimization is the displacement $s$ solving the displayed linear system, where $H$ is the Hessian matrix and $\nabla f$ the gradient. The next iterate is $p+s$. This makes the first order Taylor expansion of the gradient at the new point vanish. An invertible Hessian matrix determines a unique step; it need not give a descent direction when the Hessian matrix is indefinite.