2011 Fiscal Year Final Research Report
Applications of the theory of reproducing kernels to the Tikhonov regularization
| 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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| 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 |
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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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[Journal Article] Interpolation and sampling2011
Author(s)
Butzer, P. L., Ferreira, P. J. S. G., Higgins, J. R., Saitoh, S., Schmeisser, G., Stens, R. L. E. T. Whittaker, K. Ogura and their followers
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Journal Title
Fourier Anal. Appl.
Volume: 17no.2
Pages: 320-354
Peer Reviewed
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[Book] World Sci2009
Author(s)
Fjiwara, H., Matsuura, T., Saitoh, S., Sawano, Y.
Total Pages
574-583
Publisher
Hackensack
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