Development of Fast Numerical Algorithms for Elementary and Special Functions retaining High Reliability, High Accuracy and High Portability

2015 Fiscal Year Final Research Report

• Project/Area Number: 24700015
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Fundamental theory of informatics
• Research Institution: Teikyo Heisei University (2014-2015); Waseda University (2012-2013)
• Principal Investigator: Yamanaka Naoya 帝京平成大学, 現代ライフ学部, 助教 (90548877)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 高精度計算 / 誤差解析 / 精度保証付き数値計算

Outline of Final Research Achievements

The purpose of this research is to develop a framework of 4H-Algorithm for some elementary and special functions. Here, the 4H-Algorithm means a fast numerical algorithm retaining high reliability, high accuracy and high portability. In this research, we have proposed algorithms based on error free transformations for real elementary functions. Moreover, we succeeded in developing algorithms for some special functions based on an integration over semi-infinite interval, for example, the modified Bessel function of the second kind.

Free Research Field

数値解析