Automatic differentiation of limit functions

摘要

Automatic differentiation can be used to evaluate the derivatives of and set up Taylor series for implicitly defined functions and maps. The author provides several examples of how this works, within the context of the MXYZPTLK class library, and discusses its extension to inverse functions. The techniques of automatic differentiation and differential algebra are rapidly becoming a standard part of accelerator physicists' arsenals. (ERA citation 18:027003)