Fast and accurate algorithms for solving eigenvalue problems

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K11343
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60100:Computational science-related
• Research Institution: Fukuoka Institute of Technology
• Principal Investigator: Miyata Takafumi 福岡工業大学, 情報工学部, 准教授 (90581645)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 高速高精度アルゴリズム / 固有値問題 / 並列計算

Outline of Final Research Achievements

We study numerical algorithms for solving eigenvalue problems.
(1) Large-scale eigenvalue problems arise in network analysis and are needed to be solved. We develop a fast algorithm for solving the problems. Numerical results on a parallel computer show that our algorithm can compute solutions of the problems faster compared to the existing algorithms. (2) We analyze the convergence property of the existing fast algorithm for solving eigenvalue problems. Our analysis clarifies the point that the algorithm is specialized for computing particular solutions of the problems. This result suggests that the algorithm and the other existing algorithms should be selectively used depending on target solutions. (3) We develop an iterative algorithms for solving large-scale generalized Hermitian eigenvalue problems. Our algorithm shows the faster convergence than the existing algorithms and thus requires lesser computational time.

Free Research Field

計算科学

Academic Significance and Societal Importance of the Research Achievements

固有値問題は応用分野に応じて多様な形式を有する複合的な工学問題であり、電子状態計算や構造解析、安定性解析など、様々な応用分野に現れる。特に近年の計算機の発達に伴って、扱う問題規模や複雑さが著しく増加しており、より速く、より正確に問題を解けるような高速高精度アルゴリズムの開発が求められる。
本研究は応用分野に現れる固有値問題を解くため、高速高精度アルゴリズムの研究に取り組んだ。本研究で開発を行ったアルゴリズムに関する研究は、応用諸分野に役立てるための基盤であり、今後益々発展に取り組む必要がある。