Computational harmonic analysis - approximation of function
| Project/Area Number |
24540184
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
OKADA MASAMI 首都大学東京, 理工学研究科, 教授 (00152314)
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| Co-Investigator(Kenkyū-buntansha) |
MORITOU SHINYA 奈良女子大学, 自然科学系, 教授 (30273832)
UENO TOSHIHIDE 東京大学, 医学(系)研究科(研究院), 助教 (40381446)
SAWANO YOSHIHIRO 首都大学東京, 大学院理工学研究科, 准教授 (40532635)
立澤 一哉 北海道大学, 理学(系)研究科(研究院), 准教授 (80227090)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 実解析学 / サンプリング定理 / 多変数関数近似 / データ解析 / 不規則格子点 / 正定型関数 / サンプリング補間 / ラグランジュ補間関数 / 基底関数 / 近似誤差評価 / Greedy ｱﾙｺﾞﾘｽﾞﾑ / 逆問題 |
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| Outline of Final Research Achievements |
We investigated the general sampling theorem for scattered data in multi dimensional Euclidean spaces, which means the reconstruction of unknown functions from their data observed on irregularly scattered infinite points. In particular, we established the mathematical theory of the method of using suitable positive definite functions. In fact we have succeeded in proving an optimal
approximate error estimate previously known for the regular sampling case and the applicability of the method. One of the key points is a breakthrough on the multi dimensional polynomial approximation.
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Report
(5 results)
Research Products
(9 results)
