Toward Low Static Memory Jacobian Accumulation
نویسندگان
چکیده
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.
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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