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2023 Fiscal Year Final Research Report

Fusion of Iterative Solvers for Linear Equations with Sparse Matrices and Verified Numerical Computation Methods

Research Project

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Project/Area Number 20H04195
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 60090:High performance computing-related
Research InstitutionShibaura Institute of Technology

Principal Investigator

Ozaki Katsuhisa  芝浦工業大学, システム理工学部, 教授 (90434282)

Co-Investigator(Kenkyū-buntansha) 荻田 武史  東京女子大学, 現代教養学部, 教授 (00339615)
相原 研輔  東京都市大学, 情報工学部, 准教授 (70735498)
Project Period (FY) 2020-04-01 – 2023-03-31
Keywords精度保証付き数値計算 / 連立一次方程式 / 反復解法
Outline of Final Research Achievements

To enable verified numerical computations for iterative solvers of systems of linear equations with sparse coefficient matrices, we precomputed and published the maximum norm of the inverse matrices from the SuiteSparse Matrix Collection. This allows verified numerical computations to obtain tight error bounds for many problems within approximately twice the time of approximate computations (including the time for approximate computations). Additionally, we developed a mixed-precision iterative solver for systems of linear equations that does not require complex procedures to obtain very good approximate solutions from an error perspective, and demonstrated its usefulness through numerical experiments.

Free Research Field

精度保証付き数値計算

Academic Significance and Societal Importance of the Research Achievements

SuiteSparse Matrix Collectionにある行列は、科学技術計算において具体的に現れる行列であり、反復解法の有用性を評価するためによく使用されてきた。通常、相対残差ノルムを用いて近似解の良し悪しを議論してきたが、相対誤差の観点から精度を議論できるようになり、新たな視点で反復解法を評価し、より深い精度の議論が可能となった。反復解法は多くの分野のシミュレーションにおいて必須であり、この研究で可能としたこと、提案した反復解法は将来のシミュレーション技術の発展に寄与するものである。

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Published: 2025-01-30  

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