2024/04/11 by Uwe Naumann, Naumann, Uwe · 1 citation
Engineering · Mathematics · #Computational Engineering #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #Finance #Geometric and Algebraic Topology #Machine Learning (cs.LG) #Robotic Mechanisms and Dynamics #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2406.11862
openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The efficient computation of Jacobians represents a fundamental challenge in computational science and engineering. Large-scale modular numerical simulation programs can be regarded as sequences of evaluations of in our case differentiable subprograms with corresponding elemental Jacobians. The latter are typically not available. Tangent and adjoint versions of the individual subprograms are assumed to be given as results of algorithmic differentiation instead. The classical (Jacobian) Matrix Chain Product problem is reformulated in terms of matrix-free Jacobian-matrix (tangents) and matrix-Jacobian products (adjoints), subject to limited memory for storing information required by latter. All numerical results can be reproduced using an open-source reference implementation.