2003 Fiscal Year Final Research Report Summary
Studies on fast numerical calculation with verification
| 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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| Keywords | Verified Numerical Computation / Fast Verification / Rounding Mode Controlled Computation / IEEE754 |
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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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Research Products
(15 results)
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[Publications] R.B.Kearfott, M.Neher, S.Oishi, F.Rico: "Libraries, Tools, and Interactive Systems for Verified Computations : Four Case Studies, in Numerical Software with Result Verification"Lecture Notes in Computer Science (ed. R.Alt, A.Frommer, R.B.Kearfott, W.Luther) (Springer Verlag, Heidelberg). (2004)
Description
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