Corecursive Coding of High Computational Derivatives and Power Series

TL;DR

This paper explores corecursive methods for efficiently generating and manipulating high-order derivatives and power series in automatic differentiation, including their algebraic operations and applications.

Contribution

It introduces novel corecursive coding techniques for derivatives and power series, enhancing computational methods in automatic differentiation.

Findings

Developed corecursive algorithms for derivatives and power series

Analyzed algebraic and compositional operations on these structures

Presented applications demonstrating the methods' utility

Abstract

We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic differentiation''. Two models thereof are considered, the chains of ``pure'' derivatives, and the infinite power series, similar, but algorithmically a bit different. We deal with their arithmetic/algebra, and with more convoluted procedures, such as composition and reversion. Some more specific applications of these structures are also presented.