A NEW APPROACH FOR THE EXISTENCE PROBLEM OF MINIMAL CUBATURE FORMULAS BASED ON THE LARMAN-ROGERS-SEIDEL THEOREM

作者：Hirao Masatake^*; Nozaki Hiroshi; Sawa Masanori; Vatchev Vesselin

来源：SIAM Journal on Numerical Analysis, 2012, 50(5): 2716-2728.

DOI：10.1137/110826552

• Chebyshev polynomial
• cubature formula
• Larman-Rogers-Seidel theorem
• minimal formula
• Mysovskikh theorem

In this paper we consider the existence problem of minimal cubature formulas of degree 4k+1 for spherically symmetric integrals. We prove that, for a minimal formula in sufficiently high-dimensional space, there exists some concentric sphere on which the inner product of any two distinct points is rational. By using this result, we prove that for any d %26gt;= 2 there exist no d-dimensional minimal formulas of degrees 13 and 21 for some special integral.

• 出版日期2012