Read e-book online Advances in Automatic Differentiation (Lecture Notes in PDF

By Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe Naumann, Jean Utke

ISBN-10: 3540689354

ISBN-13: 9783540689355

ISBN-10: 3540689427

ISBN-13: 9783540689423

This assortment covers advances in automated differentiation conception and perform. computing device scientists and mathematicians will know about fresh advancements in computerized differentiation concept in addition to mechanisms for the development of sturdy and robust automated differentiation instruments. Computational scientists and engineers will enjoy the dialogue of varied purposes, which supply perception into powerful thoughts for utilizing automated differentiation for inverse difficulties and layout optimization.

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Additional resources for Advances in Automatic Differentiation (Lecture Notes in Computational Science and Engineering)

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Proof. The proof constructs a bijection between RC and DAGR. Consider an arbitrary DAG as in DAGR. Let all intermediate and maximal vertices represent calls to multivariate scalar functions fi , i = 1, . . , q, operating on a global memory space p ∈ Rµ . The fi are assumed to encapsulate the ϕi from (1). Hence, the local tapes are empty since the single output is computed without evaluation of intermediate values directly from the inputs of fi . Any given instance of DAGR can thus be mapped uniquely to an instance of RC and vice versa.

The ck values are McLaurin’s coefficients of the function Φ obtained from F.

Automatic Differentiation: Applications, Theory, and Implementations, LNCSE, pp. 263–273. Springer, Berlin, Germany (2005) Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation Mike B. uk Summary. This paper collects together a number of matrix derivative results which are very useful in forward and reverse mode algorithmic differentiation. It highlights in particular the remarkable contribution of a 1948 paper by Dwyer and Macphail which derives the linear and adjoint sensitivities of a matrix product, inverse and determinant, and a number of related results motivated by applications in multivariate analysis in statistics.

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Advances in Automatic Differentiation (Lecture Notes in Computational Science and Engineering) by Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe Naumann, Jean Utke

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