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. laptop scientists and mathematicians will know about contemporary advancements in automated 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 supply perception into powerful suggestions for utilizing computerized differentiation for inverse difficulties and layout optimization.

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

**Sample text**

4. The tapes of all subroutines are empty. Hence, the cost function is composed of the costs of executing the subroutines for a given set of inputs (unit cost per subroutine) in addition to the cost of generating the required result checkpoints (unit cost per checkpoint). The values v1 , . . , v5 need to be restored in reverse order. The input values v−1 and v0 are stored in any case. With a stack of size seven at our disposal a (result-)checkpoint-all strategy solves the FCDR problem. The same optimal cost can be achieved with a stack of size four.

Keywords: Automatic differentiation, Laguerre expansion, numerical Laplace inversion 1 Introduction Automatic differentiation (AD) is having a deep impact in many areas of science and engineering. AD plays an important role in a variety of scientific applications including meteorology, solution of nonlinear systems and inverse problems. Here we are dealing with the Laplace transform inversion (Lti) in the real case. Given a Laplace transform function F(z): ∞ F(z) = 0 e−zt f (t)dt, z = Re(z) > σ0 , (1) where σ0 is the abscissa of convergence of Laplace transform, we focus on the design of algorithms which obtain f (t), at a given selection of values of t under the hypothesis that F(z) is only computable on the real axis.

Evaluating Derivatives. Principles and Techniques of Algorithmic Differentiation. SIAM (2000) 9. : ADOL–C, a package for the automatic differentiation of algorithms written in C/C++. ACM Transactions on Mathematical Software 22(2), 131–167 (1996) 10. : The adjoint data-flow analyses: Formalization, properties, and applications. In: [2], pp. 135–146. Springer (2005) 11. : To-be-recorded analysis in reverse mode automatic differentiation. Future Generation Computer Systems 21, 1401–1417 (2005) 12.

### 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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