1990 Fiscal Year Final Research Report Summary
Implementation and Development of Application of Fast Automatic Differentiation
| Project/Area Number |
63460131
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
計算機工学
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| Research Institution | The University of Tokyo |
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Principal Investigator |
IRI Masao Univ. of Tokyo, Fac . of Eng., Professor, 工学部, 教授 (40010722)
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| Co-Investigator(Kenkyū-buntansha) |
IMAI Toshiyiki Univ. of Tokyo, Fac. Of Eng ., Assistant, 工学部, 助手 (90213214)
KUBOTA Koichi Keio Univ., Fac. of Sci. and Eng., Assistant, 理工学部, 助手 (90178046)
MUROTA Kazuo Univ. of Tokyo, Fac. of Eng., Associate Professor, 工学部, 助教授 (50134466)
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| Project Period (FY) |
1988 – 1990
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| Keywords | Fast Automatic Differentiation / Numerical Differentiation / Rounding Error / Interval Analysis |
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| Research Abstract |
FAST AUTOMATIC DIFFERENTIATION (FAD) was proposed by Masao IRI in 1983. The objectives of this research are to develop a software to realize FAD and its application to real-world problems and to establish FAD as a technique of numerical computation.
The results of this research are as follows :
(1) Improvement of FAD preprocessor : In addition to the already available FORTRAN preprocessor, an operator-overloading technique by means of c++ was developed. Those two types of implementations were improved to a software system for numerical experiment. They are capable also of computing the rounding error estimates of functions and gradients and are portable to various types of computers.
(2) Rigorous theory of rounding error estimation and use of the estimation in numerical algorithms : It was theoretically proved and experimentally evidenced that, using FAD, the error estimation can be rigorous and sharper. It was pointed out how to improve the method of constructing computational graphs. Application of FAD to the solution of nonlinear equation systems and geometrical/geographical optimization problems proved the effectiveness of FAD. In fact the accuracy of the results, the computational speed, the convergence criterion, etc. Were remarkably ameliorated.
(3) Hybridization of FAD and formula manipulation : This has not yet been completed because it took longer than expected for the research described in (1) and (2).
The above-described research results have been publicized at research meetings at home and abroad, and turned out to lead this kind of research in the world.
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