2020 Fiscal Year Final Research Report
Extension of Fast Numerical Algorithms for Special Functions retaining High Reliability, High Accuracy and High Portability
| Project/Area Number |
16K16060
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
High performance computing
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| Research Institution | Meisei University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | 高精度計算 / 誤差解析 / 精度保証付き数値計算 |
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| Outline of Final Research Achievements |
The purpose of this research is to extend a framework of 4H-Algorithm for some 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 with complex variables for Gamma function, Modified Bessel function, Sinc function. Moreover, we succeeded in developing algorithm for high order differential based on the hyper dual numbers, so that we can develop the 4H-algorithm for other special functions.
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| Free Research Field |
数値解析
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| Academic Significance and Societal Importance of the Research Achievements |
複素変数に対する特殊関数の計算について，倍精度数だけを利用して（高可搬）、倍精度数のより高精度な精度を（高精度）、精度保証付きで達成する（高信頼）、既存手法より実行時間が早い（高速）、計算アルゴリズムの設計法を構築したことにより，現在使っている計算機環境のまま、僅かなソフトウエアの変更で、従来の精度の倍の結果を精度保証付きで得られ、誤りの無い解が計算できる高速なアルゴリズム（4H-Algorithm）に基づいた「安心・安全な数値結果」を利用することができるようになった．
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