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 idea and perform. desktop scientists and mathematicians will know about fresh advancements in computerized differentiation conception in addition to mechanisms for the development of strong and strong automated differentiation instruments. Computational scientists and engineers will enjoy the dialogue of assorted purposes, which supply perception into powerful options for utilizing computerized differentiation for inverse difficulties and layout optimization.

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Advances in Automatic Differentiation (Lecture Notes in - download pdf or read online

This assortment covers advances in computerized differentiation concept and perform. computing device scientists and mathematicians will know about contemporary advancements in computerized differentiation conception in addition to mechanisms for the development of sturdy and robust computerized differentiation instruments. Computational scientists and engineers will enjoy the dialogue of assorted functions, which offer perception into potent ideas for utilizing automated differentiation for inverse difficulties and layout optimization.

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Extra info for Advances in Automatic Differentiation (Lecture Notes in Computational Science and Engineering)

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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. Keywords: Forward mode, reverse mode, numerical linear algebra 1 Introduction As the title suggests, there are no new theoretical results in this paper.

DAGR is NP-complete. Proof. The idea behind the proof in [13] is the following. An algorithm for DAGR can be used to solve FCDR as follows: For K = n + p “store-all” is a solution of DAGR for C = n + p. Now decrease K by one at a time as long as there is a solution of FCDR for C = n + p. Obviously, the smallest K for which such a solution exists is the solution of the minimization version of FCDR. A given solution is trivially verified in polynomial time by counting the number of flops performed by the respective code.

The judgement C1 ∼ C2 : φ ⇒ ψ means simply {φ }C1 {ψ } ⇒ {φ }C2 {ψ }. In the assignment rule (asgn), the lhs variable may be different. Also, notice that the same conditional branches must be taken (see the if rule) and that loops be executed the same number of times (see the while rule) on the source and target to guarantee their semantics equivalence. 4 A Hoare Logic for Forward Mode AD The forward mode AD can be implemented using (1) in order to compute the derivative y˙ given a directional derivative x˙ .

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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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