A matrix algebra approach to approximate Hessians

Abstract This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The requires less computational power than interpolation-based methods and is easy to implement in programming languages such as MATLAB. As evaluations are required, the suitable use derivative-free algorithms. For reasonably structured sample sets, proven create order-$1$ accurate of full Hessian. Under more specialized structures, proved yield order-$2$ accuracy. underdetermined case, where number points fewer required interpolation, studied error bounds developed resulting partial Hessians.