Toward Low Static Memory Jacobian Accumulation

Ebadollah Varnik, Uwe Naumann, Andrew Lyons

Derivatives are essential ingredients of a wide range of numerical
algorithms. We focus on the accumulation of Jacobian matrices by Gaussian
elimination on a sparse implementation of the extended Jacobian. A
symbolic algorithm is proposed to determine the fill-in. The first
version of the new algorithm results in a speedup of five compared to
the elimination algorithm that does not exploit sparsity. On the given
computer architecture we are able to handle problems with roughly four
times the original size.