| Project/Area Number |
12650399
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
情報通信工学
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| Research Institution | Waseda University |
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Principal Investigator |
OISHI Shinichi Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (20139512)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Verified Numerical Computation / Fast Verification / Rounding Mode Controlled Computation / IEEE754 / クラスター上の高速計算 / 連立一次方程式の精度保証 / 固有値問題の精度保証 / 一般化固有値問題の精度保証 / 大規模問題 / PCクラスター / 丸め誤差 / 条件数 / 数値計算ツール / LAPACK / 連立一次方程式の数値解 / 固有値問題の数値解 / インタプリタ / 事後誤差評価 / 数値線形代数 / 行列方程式 / 固有値問題 / 特異値 / 丸め制御精度保証方式 |
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| Research Abstract |
The present researcher has shown that the addition and the product of two matrices can be calculated with verification via tow times changes of rounding mode of floating point arithmetic. Namely he has proposed a vector interval arithmetic. Furthermore, utilizing perturbation theory, which gives a posteriori error estimate, it has shown that a rigorous error bound of an approximate solution of a system of linear equations can be calculated with the same cost as that of calculating such an approximate solution. It is around from 1,000 to 10,000 speed up compared with the previous method. This method can be extended to many problems of numerical linear algebra including matrix eigenvalue problems and singular value problems. As examples, from 1,000 to 30,000 dimensional full matrix systems have been solved via PC cluster system.
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