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Gauss Quadrature Formulae

The following theorem links the Fejér-problem directly with the existence problem of multivariate Gauss-quadratures and in case of tex2html_wrap_inline3133 with the existence of a 2m-design.


stz194


stz206

Thus, for tex2html_wrap_inline3269, tex2html_wrap_inline3323 there exist no Gauss-quadratures for tex2html_wrap_inline3133 and for tex2html_wrap_inline3269, tex2html_wrap_inline3329 they do not exist for tex2html_wrap_inline3141. There might be Gauss-quadratures for m=2. But even in these cases it turns out that certain restrictions have to hold.


stz211


stz214

That is, existence is possible for tex2html_wrap_inline3355 and it is known for tex2html_wrap_inline3357.


next up previous
Next: A Two-Stage Approach Up: Existence of Cubature Formulae Previous: Spherical Designs

Joerg Fliege
Thu Dec 23 19:39:35 CET 1999