The art of differentiating computer programs: an introduction to algorithmic differentiation

摘要

A large part of my job for the last eight years has been dealing with the first-and second-order derivatives of financial instruments. Hence, I find myself intimately aware of the numerical inaccuracies and computation time complexity of finite difference techniques. Thus, it was with great anticipation that I started reading this book about a world of faster and more accurate derivatives. Chapter 1 broadly describes a motivation for algorithmic differentiation. It starts off with a few examples where derivatives are required, such as a steepest descent search in nonlinear programming, how to use the Newton algorithm for solving systems of nonlinear equations, and how to deal with constraints. Having denned some problems, the author describes manual differentiation before moving on to approximation techniques. It is in the context of finite differences that the inaccuracies introduced by finite precision floating-point numbers are analyzed.