Realizing the original formula “DE-Sinc method” in numerical computation

Professor Masaaki Sugihara
(Department of Mathematical Informatics)

Development of science technology has been supported by large-scale numerical computation using computers. Professor Sugihara developed “DE-Sinc method” that can be the powerful formula as a core of numerical computation by dramatically improving the order of computational errors. He strives to apply this new numerical computation algorithm not only in science technology but also all fields including finance and social science as a tool for numerical computation. The true aim is “to make a breakthrough in numerical computation.”

Numerical computation is vital in understanding big science and natural phenomena, and design such as global environment, life science, nanotechnology, and aerospace. However, there are always errors in numerical computation to reveal phenomena no matter how advanced the performance of computers is to derive computational results. In anticipation of the trend to minimize errors in numerical computation, Professor Sugihara focused on “Sinc Approximation” that yields extremely small errors developed by Stenger at University of Utah in US and “Double Exponential Formula = DE Formula” developed by Hidetoshi Takahashi and Masatake Mori at the University of Tokyo.

As he studied the two formulae, he noticed that a highly accurate numerical computation method with a little errors could be developed by incorporating DE transformation into numerical computation methods based on Sinc approximation. His formula named “DE-Sinc Method” allows the order of errors to be marginal and hence it further promoted development of numerical computation methods based on Sinc approximation.

He says “There is no almighty theory in numerical computation. The field of study dies out on the arrival of an almighty theory. But there is the best, if not almighty. That is what I would like to pursue.” Numerical computation is yet to be fully applied in some fields such as finance, complex network, and social science, which are becoming an exact science. Creating a new paradigm by stepping into the unexplored fields with numerical computation ---- this is the real aspiration of Professor Sugihara.