| 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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| 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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