2012 Fiscal Year Final Research Report
Breakthrough in numerical analysis and numerical computation related with infinitely-precision arithmetic
| Project/Area Number |
22340018
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
ISO Yuusuke 京都大学, 情報学研究科, 教授 (70203065)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIWARA Hiroshi 京都大学, 情報学研究科, 助教 (00362583)
KUBO Masayoshi 京都大学, 情報学研究科, 講師 (10273616)
NISHIDA Kotoba 鹿児島大学, 理工学研究科, 助教 (10274838)
SAKAJYOU Takashi 北海道大学, 理学(系)研究科(研究院), 教授 (10303603)
OONISHI Kazuei 茨城大学, 理学部, 教授 (20078554)
NAKAMURA Yoshimasa 京都大学, 情報学研究科, 教授 (50172458)
IMAI Hitoshi 徳島大学, ソシオテクノサイエンス研究部, 教授 (80203298)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 数学一般 / 応用数学 / 数値数学 / 数理モデル / 応用解析 / 数値解析 / 多倍長数値計算 / 非適切問題解析 |
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| Research Abstract |
We have shown some new results aimed to accurate scientific computationsbased on effective use of infinitely-precision arithmetic. The project study has been carried out both by theoretical approaches and computationalones. In the theory of numerical analysis, convergence of an abstract difference scheme is proved with a technique of the Banach scale, and numerical instability of difference schema are discussed from a viewpoint of proper meaning of the CFL condition. In computation, we have obtained accurate numerical results for the problems appeared in the particle physics and the eigen-value problems. The GPGPU programmingsare also discussed in order to realize fast computational environment.
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