2019 Fiscal Year Final Research Report
Research and development of a verification method for ill-conditioned linear systems
| Project/Area Number |
17K12692
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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 | Chuo University (2018-2019)
National Institute of Advanced Industrial Science and Technology (2017) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| 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 |
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| 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.
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| Free Research Field |
精度保証付き数値計算
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| 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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