| Project/Area Number |
11650072
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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 |
Engineering fundamentals
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| Research Institution | CHUO UNIVERSITY |
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Principal Investigator |
KUBOTA Koichi Chuo University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (90178046)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | automatic differentiation / storage size reduction / numerical information processing / various data types / quality of computation / 領域削除 |
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| Research Abstract |
"Quality control of computation" in the title means to control the computation calculating "the final value" in a permissible error as fast as possible.
The well-known multi-precision floating-point arithmetic operations would be sufficient to improve the accuracy of the final value. However, its accuracy is still unknown since it is different from the accuracy of each arithmetic operation.
The purpose of this research is to investigate a system called "numerical information system" that computes the numerical values in the permissible error, or in the desired accuracy, as fast as possible by means of control of accuracy of individual multi-precision floating-point arithmetic operations executed in the whole computation.
The following two policies were provided by using fundamental techniques : automatic differentiation for sensitivity analysis and interval operation for rigorous upper bounds. The first policy is that we improve accuracy (instead of speed) of arithmetic operations whose results have large influences on the final value, and that we improve speed (instead of accuracy) of arithmetic operations whose results have small influences. The second policy is to implement an algorithm for reducing the size of the storage required for fast automatic differentiation.
We had two results. The first result is a prototype system that can automatically iterate the following two steps to get the final values : the sensitivity analysis and control of the accuracy of each arithmetic operation. The second result is an implementation of the reduction algorithm of the storage size required by fast automatic differentiation with the 'fork' and 'semaphore' UNIX system calls.
The results are applied to conjugate gradient computations, and they will be applied to several numerical computations : the Jacobi-Davidson method for eigenvalue computations, error analysis on boundary value problem of partial or ordinary differential equations, geographical optimization problems, etc.
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