Optimized Jacobian Accumulation Techniques
نویسنده
چکیده
Jacobian matrices can be accumulated using either the forward or reverse mode of Automatic Di erentiation. Alternatively, derivative code can be generated to compute the Jacobian directly at the current argument. The minimisation of the corresponding number of arithmetic operations leads to a computationally hard combinatorial optimisation problem. A method for its approximate solution by dynamic programming will be discussed brie y. It results in a speedup of three and more for most problems.
منابع مشابه
Exploitation of structural sparsity in algorithmic differentiation
The background of this thesis is algorithmic differentiation (AD) [GW08] of in practice very computationally expensive vector functions F : R ⊇ D → R given as computer programs. Traditionally, most AD software1 provide forward and reverse modes of AD for calculating the Jacobian matrix ∇F (x) accurately at a given point x on some kind of internal representation of F kept on memory or hard disk....
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