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math.NA2012★ 1 cited
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…
math.NA2011
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…
math.NA2011★ 6 cited
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…