Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph

Authors:
Uwe Naumann
Affiliations:
Argonne National Laboratory
Venue:
Mathematical Programming: Series A and B
Year:
2004

Citing 0
Cited 12

Towards differentiation-enabled Fortran 95 compiler technology

Proceedings of the 2003 ACM symposium on Applied computing
Jacobian code generated by source transformation and vertex elimination can be as efficient as hand-coding

ACM Transactions on Mathematical Software (TOMS)
A differentiation-enabled Fortran 95 compiler

ACM Transactions on Mathematical Software (TOMS)
An efficient overloaded implementation of forward mode automatic differentiation in MATLAB

ACM Transactions on Mathematical Software (TOMS)
Efficient reversal of the intraprocedural flow of control in adjoint computations

Journal of Systems and Software - Special issue: Selected papers from the 4th source code analysis and manipulation (SCAM 2004) workshop
Term Graphs for Computing Derivatives in Imperative Languages

Electronic Notes in Theoretical Computer Science (ENTCS)
Computing sparse Hessians with automatic differentiation

ACM Transactions on Mathematical Software (TOMS)
OpenAD/F: A Modular Open-Source Tool for Automatic Differentiation of Fortran Codes

ACM Transactions on Mathematical Software (TOMS)
Optimal vertex elimination in single-expression-use graphs

ACM Transactions on Mathematical Software (TOMS)
Markowitz-type heuristics for computing Jacobian matrices efficiently

ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Coupling tangent-linear and adjoint models

ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
A graph algorithm for linearizing simulink models

Proceedings of the 2013 Summer Computer Simulation Conference

Quantified Score

Hi-index	0.00

Visualization

Abstract

The accumulation of the Jacobian matrix F’ of a vector function *** equation here *** can be regarded as a transformation of its linearized computational graph into a subgraph of the directed complete bipartite graph Kn,m. This transformation can be performed by applying different elimination techniques that may lead to varying costs for computing F’. This paper introduces face elimination as the basic technique for accumulating Jacobian matrices by using a minimal number of arithmetic operations. Its superiority over both edge and vertex elimination methods is shown. The intention is to establish the conceptual basis for the ongoing development of algorithms for optimizing the computation of Jacobian matrices.