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)
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The generation of optimized code for evaluating the Jacobian matrix of a vector function is known to result in a remarkable speedup of three and more compared to standard methods of Automatic Differentiation in most cases. So far, this optimization has been built on the elimination of vertices in the computational graph. We show that vertex elimination in general does not lead to optimal Jacobian code. We introduce two new elimination methods and demonstrate their superiority over the vertex elimination approach.