Constructing cubature formula and its application to design of experiments
Project/Area Number |
25870756
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
Algebra
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Research Institution | Aichi Prefectural University (2014-2015) Tokyo Woman's Christian University (2013) |
Principal Investigator |
HIRAO Masatake 愛知県立大学, 情報科学部, 准教授 (90624073)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
Keywords | cubature公式 / 最適計画 / 回転可能計画 / 球面上のデザイン / ユークリッド空間上のデザイン / 作用素型cubature公式 / Cubature公式 / QMCデザイン / 確率点過程 / Laplace作用素型cubature公式 |
Outline of Final Research Achievements |
We consider a novel type of cubature formulas called operator-type cubature formulas. We give a lower bound for the number of points needed, and discuss analytic conditions for equality, together with tight illustrations for Laplacian-type cubature. On the other hand, we also consider constructing classical cubature problems of higher degree cases. We provides a systematic treatment of a group-theoretic approach for constructing classical cubature formulas and designs. Moreover, we give a method of reconstruction of formulas via combinatorial designs.
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Report
(4 results)
Research Products
(20 results)