| Project/Area Number |
62302007
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
YAMAMOTO Tetsuro Professor Department of Mathematics, Faculty of Science, Ehime University, 理学部, 教授 (80034560)
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| Co-Investigator(Kenkyū-buntansha) |
MIMURA Masayasu Professor, Faculty of Science, Hiroshima University, 理学部, 教授 (50068128)
KAWARADA Hideo Professor, Faculty of Engineering,Chiba University, 工学部, 教授 (90010793)
USHIJIMA Teruo Professor, University of Electro-Communications, 教授 (10012410)
IRI Masao Professor, Faculty of Engineering, Tokyo University, 工学部, 教授 (40010722)
森 正武 筑波大学, 電子情報工学系, 教授 (20010936)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥9,500,000 (Direct Cost: ¥9,500,000)
Fiscal Year 1988: ¥4,500,000 (Direct Cost: ¥4,500,000)
Fiscal Year 1987: ¥5,000,000 (Direct Cost: ¥5,000,000)
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| Keywords | Nonlinear iterative method / Ball-convergence theorem / Free boundary problems / Structure of solution of partial differential equations / Fast automatic differentiation / 誤差評価 / 計算数学 / 応用解析 / 応用数学 / 数値解析 / 誤差解析 / 解の存在定理 / 反復法 |
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| Research Abstract |
This is a co-operative study on computational mathematics and applied analysis done by 17 researchers. Among others, the head investigator Yamamoto studied Krasnoselskii-Zincenko type iterative method for solving the equation f+g=O in a banach space, where f is Frechet-differentiable and g is not. Under Kantorovich type assumptions, he improved the results of Zabrejko-Nguen (1987), determined a convergence domain for the iteration and found a necessary and sufficient condition for convergence of the method. Furthermore, he obtained a ball-convergence theorem which improves a classical semi-local convergence theorem for the equation f=O. These results were done with a Chinese student X.Chen and were reported in the International Conference on Numerical Mathematics, Singapore, May 1988, the 13-th International Symposium on Mathematical Programming, Tokyo, September 1988, etc.
As other subjects, M.Iri proposed a self-validating numerical method based on fast automatic differentiation. T.Ushijima analyzed an approximate problem arising in the analysis of surface of the wave of water in a box. H.Kawarada proposed numerical methods for some free boundary problems. M.Mimura gave theoretical analysis for solution of nonlinear partial dofferential equations as well as computer simulations.
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