Overview

Masatake Mori (1937–2017) was a prominent Japanese mathematician specializing in numerical analysis. He held professorial posts at the University of Tokyo and at Kyoto University. His research influenced many areas of computational mathematics, most notably numerical quadrature.

Main contribution: the double exponential integration formula

Mori is widely credited with developing what is commonly called the double exponential (DE) integration formula, a change-of-variable technique that accelerates the convergence of numerical quadrature. The approach is often associated with the name tanh-sinh or the Takahasi–Mori transformation and is regarded as one of the most effective general-purpose methods for numerical integration, particularly when high accuracy is required.

Characteristics and why it works

The DE method uses a transformation that causes the integrand to decay double-exponentially at transformed endpoints. This rapid decay makes simple quadrature rules (like the trapezoidal rule) extraordinarily accurate after transformation. The method performs especially well for integrals with endpoint singularities, infinite integration ranges, or extremely smooth integrands where very high precision is sought.

Other work, collaborations, and influence

Mori contributed to related computational techniques and published joint studies with colleagues, including Masaaki Sugihara. His work intersects with Sinc approximation, transformed quadrature schemes, and strategies for stable high-precision computation. These ideas have been incorporated into numerical libraries and influenced later research on efficient integration algorithms.

Applications and examples

  • Accurate evaluation of definite integrals with endpoint singularities.
  • Integration over infinite intervals by mapping to finite domains with rapid decay.
  • High-precision computations in physics, engineering, and computational number theory.

Legacy and notable facts

Mori's double exponential formula remains a standard tool in the numerical analyst's repertoire because of its simplicity and power. His academic positions at leading Japanese universities helped disseminate these techniques through teaching and collaboration. Researchers and practitioners continue to cite and adapt the DE approach when conventional quadrature methods struggle to reach required precisions.

For institutional information and further reading, see the pages of the University of Tokyo, Kyoto University, surveys of numerical analysis, introductions to numerical integration, and works by collaborators such as Masaaki Sugihara.