论文信息 - Optimal lower bounds for cubature error on the sphere S2

Optimal lower bounds for cubature error on the sphere S2

We show that the worst-case cubature error E(Q"m;H^s) of an m-point cubature rule Q"m for functions in the unit ball of the Sobolev space H^s=H^s(S^2),s>1, has the lower bound E(Q"m;H^s)>=c"sm^-^s^2, where the constant c"s is independent of Q"m and m. This lower bound result is optimal, since we have established in previous work that there exist sequences (Q"m"("n"))"n"@?"N of cubature rules for which E(Q"m"("n");H^s)==c"sm^-^s^2. The construction uses results about packings of spherical caps on the sphere.

Ian H. Sloan | Kerstin Hesse | I. Sloan | Kerstin Hesse

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