Optimal Estimation of Jacobian and Hessian Matrices That Arise in Finite Difference Calculations
Optimal Estimation of Jacobian and Hessian Matrices That Arise in Finite Difference Calculations
In this paper, the problem of estimating Jacobian and Hessian matrices arising in the finite difference approximation of partial differential equations is considered.Using the notion of computational molecule or stencil, schemes are developed that require the minimum number of differences to estimate these matrices.A procedure applicable to more complicated structures …