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Special section: Automatic differentiation and its applications

机译：特殊部分：自动区分及其应用

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摘要

The evaluation of derivatives of mathematical functions is a crucial ingredient in a variety of computational techniques in numerical simulations. Gradients, Jacobians, or higher-order derivatives are needed, for instance, in the solution of nonlinear systems of equations, differential and differential-algebraic equations, or optimization problems, to name a few. In large-scale computer simulations which are increasingly becoming an important part of many scientific investigations, the function describing the system of interest is typically not available in analytic form. That is, there is generally no explicit formula relating the function to its input variables. Most likely, this function is given by a highly complex scientific computer code capable of evaluating the function at certain arguments. Typically, these codes are written in a high-level programming language such as Fortran, C, or MATLAB. How do we efficiently and accurately evaluate derivatives for functions implemented by such computer programs?
机译：数学函数导数的评估是数值模拟中各种计算技术的重要组成部分。例如，在非线性方程组，微分和微分代数方程组或优化问题的解决方案中，需要使用梯度，雅可比或高阶导数。在越来越成为许多科学研究的重要组成部分的大规模计算机仿真中，描述目标系统的功能通常无法以解析形式获得。也就是说，通常没有明确的公式将该函数与其输入变量相关联。最有可能的是，此功能由高度复杂的科学计算机代码提供，该代码可以在某些参数上评估该功能。通常，这些代码是用高级编程语言（例如Fortran，C或MATLAB）编写的。我们如何有效，准确地评估由此类计算机程序实现的功能的导数？

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