| Project/Area Number |
21540111
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Gunma University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MATSUURA Tsutomu 群馬大学, 大学院・工学研究科, 准教授 (80181692)
WATANABE Syuuji 群馬大学, 大学院・工学研究科, 教授 (90222405)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 再生核 / チホノフ正則化法 / 逆問題 / アルゴリズム / 数値解析 / 近似解積分方程式 / 微分方程式 / 積分方程式 / 行 / 近似解 / チコノフ正則化法 / 一般化逆 / 有界線形作用素 / 近似法 / 離散化 / 離散微分方程式 / 特異積分方程式 / 境界値問題 |
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| Research Abstract |
We obtained the concept of discrete differential equations and derived various concrete results. For a finite number of input data, we obtain a new concept that we can give natural input data as other input data. We introduced the new definition of general fractional functions and their representations, and methods how to calculate them practically, by computers. We gave the approximate solutions of integral equations with convolution type kernels and with Toeplitz and Hankel kernels. New convolutions and related convolution norm inequalities were derived. We wrote a new research book manuscript with 314 pages.
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