2011/03/06 by Masatake Hirao, Hirao, Masatake, Hiroshi Nozaki +5
Computer Science · Mathematics · #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1103.1111
openalex publication_date 2011/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 prove that for sufficiently large dimensional minimal formulas, any two distinct points on some concentric sphere have inner products all of which are rational numbers. By applying this result we prove that for any d > 2 there exist no d-dimensional minimal formulas of degrees 13 and 21 for some special integral.