6 citations · 14 across the 7 of their papers we have counts for
4 papers · 1 filter
Remarks on Hilbert identities, isometric embeddings, and invariant cubature
Hiroshi Nozaki, Masanori Sawa
Victoir (2004) developed a method to construct cubature formulae with various combinatorial objects. Motivated by this, we generalize Victoir's method with one more combinatorial o…
On positive cubature rules on the simplex and isometric embeddings
Masanori Sawa, Yuan Xu
Positive cubature rules of degree 4 and 5 on the -dimensional simplex are constructed and used to construct cubature rules of index 8 or degree 9 on the unit sphere. The latter…
A new approach for the existence problem of minimal cubature formulas based on the Larman-Rogers-Seidel theorem
Masatake Hirao, Hiroshi Nozaki, Masanori Sawa +1
In this paper we consider the existence problem of cubature formulas of degree 4k+1 for spherically symmetric integrals for which the equality holds in the Möller lower bound. We p…
Note on cubature formulae and designs obtained from group orbits
Hiroshi Nozaki, Masanori Sawa
In 1960, Sobolev proved that for a finite reflection group G, a G-invariant cubature formula is of degree t if and only if it is exact for all G-invariant polynomials of degree at…