A derivative measures how an output changes when an input changes. That sentence is simple, but it is one of the main ideas behind numerical computing, optimization, machine...
| Section | Title |
|---|---|
| 1 | Chapter 1. Introduction |
| 2 | Numerical Differentiation |
| 3 | Symbolic Differentiation |
| 4 | Automatic Differentiation |
| 5 | Accuracy, Complexity, and Stability |
| 6 | Historical Development |
| 7 | Applications Across Science and Engineering |
Chapter 1. IntroductionA derivative measures how an output changes when an input changes. That sentence is simple, but it is one of the main ideas behind numerical computing, optimization, machine...
Numerical DifferentiationNumerical differentiation estimates derivatives by evaluating a function at nearby input values. It treats the function as a black box. The method does not need access to the...
Symbolic DifferentiationSymbolic differentiation computes derivatives by manipulating expressions. The input is a formula. The output is another formula.
Automatic DifferentiationAutomatic differentiation computes derivatives by applying the chain rule to the operations of a program. The input is ordinary code that computes a value. The output is code,...
Accuracy, Complexity, and StabilityDerivative computation is not only a mathematical problem. It is also a numerical and systems problem. A derivative method must answer three questions simultaneously:
Historical DevelopmentAutomatic differentiation developed from a simple observation: a numerical computation already contains the structure needed to compute its derivative. The program evaluates...
Applications Across Science and EngineeringAutomatic differentiation became important because derivatives are required everywhere numerical models are optimized, controlled, calibrated, or analyzed. Once a system can...