Reformulation and expanding application of the Sinc methods

2023 Fiscal Year Final Research Report

• Project/Area Number: 17K14147
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: Hiroshima City University
• Principal Investigator: Okayama Tomoaki 広島市立大学, 情報科学研究科, 准教授 (80587866)
• Project Period (FY): 2017-04-01 – 2024-03-31
• Keywords: 数値解析

Outline of Final Research Achievements

In comparison to existing general methods, the Sinc methods have been known to be highly efficient for analytic functions, which often appear in the field of natural science and engineering. This project contributed the Sinc methods in the following points: (a) extended the Sinc methods to the system of equations, (b) improved the variable transformation combined with the Sinc methods, and (c) developed self-validating numerics based on the Sinc methods. In particular, in the case of (a), we reformulated the Sinc methods to avoid being complicated in implementation.

Free Research Field

数値解析

Academic Significance and Societal Importance of the Research Achievements

Sinc法は，現実でよく現れる関数の性質をうまく使って，汎用技術を遙かに上回る高性能を実現できる計算法である．本研究ではこのSinc法の弱点を克服しさらに発展を行うものである．実装に難があった部分を改善したため，数値計算ライブラリの実装が容易になっている．さらに近似誤差を（見積もりではなく）数学的な不等式によって厳密かつ計算可能な形で評価したため，精度保証付き数値計算も可能になった．このように，本研究で理論的に得られた結果は応用でも有用な内容となっている．