Download PDF by Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe: Advances in Automatic Differentiation (Lecture Notes in

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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 computerized differentiation thought and perform. machine scientists and mathematicians will find out about contemporary advancements in computerized differentiation thought in addition to mechanisms for the development of sturdy and robust computerized differentiation instruments. Computational scientists and engineers will enjoy the dialogue of assorted purposes, which offer perception into potent techniques 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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Instead, it is a collection of results on derivatives of matrix functions, expressed in a form suitable for both forward and reverse mode algorithmic differentiation (AD) [8] of basic operations in numerical linear algebra. All results are derived from first principles, and it is hoped this will be a useful reference for the AD community. The paper is organised in two sections. The first covers the sensitivity analysis for matrix product, inverse and determinant, and other associated results. Remarkably, most of these results were first derived, although presented in a slightly different form, in a 1948 paper by Dwyer and Macphail [4].

For a given statement s, the Hoare triple {φ }s{ψ } means the execution of s in a state satisfying the pre-condition φ will terminate in a state satisfying the post-condition ψ . The conditions φ and ψ are first order logic formulas called assertions. Hoare proofs are compositional in the structure of the language in which the program is written. In this work, we consider a WHILE-language composed of assignments, if and while statements and in which expressions are formed using the basic arithmetic operations (+,-,*,/).

IEEE Computer Society (2002) 2. : ADMIT-1: Automatic differentiation and MATLAB interface toolbox. ACM Transactions on Mathematical Software 26(1), 150–175 (2000) 3. : Some applications of matrix derivatives in multivariate analysis. Journal of the American Statistical Association 62(318), 607–625 (1967) 4. : Symbolic matrix derivatives. The Annals of Mathematical Statistics 19(4), 517–534 (1948) 5. : An efficient overloaded implementation of forward mode automatic differentiation in MATLAB. ACM Transactions on Mathematical Software 32(2), 195–222 (2006) 6.

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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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