Derivatives play a critical role in computational statistics, examples being Bayesian
inference using Hamiltonian Monte Carlo sampling and the training of neural networks …

The advent of high-speed computers and sophisticated software tools has made the
computation of derivatives for functions defined by evaluation programs both easier and …

We review the methods and applications of automatic differentiation, a research and
development activity, which has evolved in various computational fields since the mid …

“How sensitive are the values of the outputs of my computer program with respect to
changes in the values of the inputs? How sensitive are these first-order sensitivities with …

Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

An introduction to both automatic differentiation and object-oriented programming can enrich
a numerical analysis course that typically incorporates numerical differentiation and basic …

The C++ package ADOL-C facilitates the evaluation of first and higher derivatives of vector
functions that are defined by computer programs written in C or C++ by means of …

Algorithmic differentiation (AD), also known as automatic differentiation, is a technology for
accurate and efficient evaluation of derivatives of a function given as a computer model. The …

CryptoNets and subsequent work have demonstrated the capability of homomorphic
encryption (HE) in the applications of private artificial intelligence (AI). In convolutional …

Automatic, or algorithmic, differentiation addresses the need for the accurate and efficient
calculation of derivative values in scientific computing. To this end procedural programs for …