2012 Fiscal Year Final Research Report
A study of combinatorial constructions and geometric characterizations of cubature formulas
| Project/Area Number |
22740062
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
SAWA Masanori 名古屋大学, 情報科学研究科, 助教 (50508182)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 求積公式 / デザイン / 直交多項式の零点 |
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| Research Abstract |
We presented a number-theoretic characterization of the configuration of points of a minimal cubature formula, as well as some existence and non-existence results on such formulas of small degrees, by unifying techniques that have been developed in numerical analysis, algebraic combinatorics, discrete geometry and so on. We also characterize a minimal cubature formula whose point set consists of orbits of a finite irreducible reflection group.
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