Constructing cubature formula and its application to design of experiments

2015 Fiscal Year Final Research Report

• 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
• 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
• 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

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.

Free Research Field

数学