Software for estimating sparse Jacobian matrices
ACM Transactions on Mathematical Software (TOMS)
Smallest-last ordering and clustering and graph coloring algorithms
Journal of the ACM (JACM)
Algorithm 636: FORTRAN subroutines for estimating sparse Hessian matrices
ACM Transactions on Mathematical Software (TOMS)
ADMIT-1: automatic differentiation and MATLAB interface toolbox
ACM Transactions on Mathematical Software (TOMS)
Sourcebook of parallel computing
Approximating Hessians in unconstrained optimization arising from discretized problems
Computational Optimization and Applications
The effect of shocks on second order sensitivities for the quasi-one-dimensional Euler equations
Journal of Computational Physics
Inexact trust region PGC method for large sparse unconstrained optimization
Computational Optimization and Applications
ColPack: Software for graph coloring and related problems in scientific computing
ACM Transactions on Mathematical Software (TOMS)
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The solution of a nonlinear optimization problem often requires an estimate of the Hessian matrix for a function f. In large scale problems, the Hessian matrix is usually sparse, and then estimation by differences of gradients is attractive because the number of differences can be small compared to the dimension of the problem. In this paper we describe a set of subroutines whose purpose is to estimate the Hessian matrix with the least possible number of gradient evaluations.