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2019 Fiscal Year Final Research Report

Research and development of a verification method for ill-conditioned linear systems

Research Project

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Project/Area Number 17K12692
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field High performance computing
Research InstitutionChuo University (2018-2019)
National Institute of Advanced Industrial Science and Technology (2017)

Principal Investigator

Minamihata Atsushi  中央大学, 理工学部, 助教 (70754787)

Project Period (FY) 2017-04-01 – 2020-03-31
Keywords精度保証付き数値計算 / 悪条件連立一次方程式 / 誤差評価
Outline of Final Research Achievements

We developed a verification method for ill-conditioned linear systems. In particular, we focus on large and ill-conditioned linear systems and proposed a verification method. We showed our proposed method gives tighter error bounds than previous methods in Higham’s test matrices.
We developed a verification method for symmetric saddle point linear systems using null space method and verification methods for a basis of the null space of a matrix.

Free Research Field

精度保証付き数値計算

Academic Significance and Societal Importance of the Research Achievements

科学技術計算において,連立一次方程式を解く事は最も基本的な問題であり,解の信頼性を担保する技術の開発は重要である.今後,計算機の性能の向上に伴いより大規模な問題を解くことが予想される.その際に,丸め誤差により解の信頼性が損なわれる.本研究は解の信頼性の向上に寄与する研究である.また,本研究成果の一部は精度保証付き数値計算のソフトウェアのINTLABに組み込まれ,多くのユーザの精度保証付き数値計算に利用されている.

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Published: 2021-02-19  

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