Double-Exponential transformation: A quick review of a Japanese tradition

TL;DR

This paper reviews the history and mathematical foundations of double exponential transformation methods, such as tanh-sinh quadrature and DE-Sinc, highlighting their development in Japan for numerical computation.

Contribution

It provides a concise overview of the origins and mathematical principles of DE-based numerical methods, emphasizing their Japanese development.

Findings

DE methods are highly effective for numerical integration.

Japanese research has significantly advanced DE transformation techniques.

The paper clarifies the mathematical ideas behind DE-based methods.

Abstract

This paper is a short introduction to numerical methods using the double exponential (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The DE-based methods for numerical computation have been developed intensively in Japan and the objective of this paper is to describe their history in addition to the underlying mathematical ideas.