sparseHessianFD: An R Package for Estimating Sparse Hessian Matrices

Abstract

Sparse Hessian matrices occur often in statistics, and their fast and accurate estimation can improve efficiency of numerical optimization and sampling algorithms. By exploiting the known sparsity pattern of a Hessian, methods in the sparseHessianFD package require many fewer function or gradient evaluations than would be required if the Hessian were treated as dense. The package implements established graph coloring and linear substitution algorithms that were previously unavailable to R users, and is most useful when other numerical, symbolic or algorithmic methods are impractical, inefficient or unavailable.

Keywords

• sparse Hessians
• sparsity
• computation of Hessians
• graph coloring
• finite differences
• differentiation
• complex step