1996 Fiscal Year Final Research Report Summary
INVERSE PROBLEMS OF SCATTERING : MATHEMATICS,NUMERICAL ANALYSIS AND GRAPHICS
| Project/Area Number |
07404004
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | Osaka University |
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Principal Investigator |
IKAWA Mitsuru Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (80028191)
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| Co-Investigator(Kenkyū-buntansha) |
MORIOKA Tatsushi Graduate School of Sciences, Osaka Univ., Assist., 大学院・理学研究科, 助手 (80239631)
ISOZAKI Hiroshi Graduate School of Sciences, Osaka Univ., Assoc.Prof., 大学院・理学研究科, 助教授 (90111913)
MATSUMURA Akitaka Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (60115938)
SAKANE Yusuke Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (00089872)
KOTANI Shin-ichi Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (10025463)
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| Project Period (FY) |
1994 – 1996
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| Keywords | Scattering / Inverse problem / Numerical analysis / Greobner basis / Einstein metric / Schrodinger operators |
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| Research Abstract |
Concerning the inverse problems for Schrodinger operatores, H.Isozaki studied deeply and got very important results. Starting from the idea of Faddeev, Isozaki made clear the relationship between the potential of Schrodinger operators and the scattering amplitude. This relationship shown by Isozaki gives a representation of the solution of the inverse problem for the Schrodinger operators. He was invited to several international conferences and was given a high evaluation.
Concerning the another core of our research, that is, numerical analysis, we introduced computers of Silicon Graphic Co.Ltd., Chalenge Indigo 2 and Indy. By the leadership of Sakane, with cooperation of graduate students (especially with Senda), we studied algorism for getting Greobner basis. Needless to say, Greobner basis play an essential role in various problems related to polynomial rings. But in order to get Greobner basis explicitely for given concrete problems, it becomes a huge computation and it takes a lot of time. So, it is very important to improve algorithm into a efficient ones.
We succeeded to make a new algorism, named GRASIS,which enable us to acheive computation of Greobner basis much faster than before. As an application of our invention of new algorism GRASIS,we found new Einstein metrics.
We have to confess that the term of our research has ended before we set about numerical analysis of inverse scattering problems. We shall continue the numerical study of inverse problems.
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